Start with pre-made Characters
By which I don't mean generic characters that could be in any fantasy story, but by creating a character specifically for each of your children. These characters should be based around the characters from movies and TV shows they each seem to be drawn most toward. It's not the perfect fit that character creation is, but it can let you leap over the hurdles that character creation presents to a new player and let your children get right into the game. Your child's statement about it feeling exactly like a movie is what you want to most emulate.
Use essentials classes only, specifically MBA focused ones
Essentials classes (the Knight, the Slayer, the Warpriest for example) are built around having strong class features (always on) vs. making choices between how to use encounter and daily powers to most benefit the party. They work best in Heroic Tier (levels 1-10) and are strong classes that do not require as much optimization as the AEDU classes do. more importantly they focus on what are iconic archetypes both within and without of D&D. The Knight and the Slayer for example are both actually sub-classes of the traditional fighter. The first wears heavy armor and is all about protecting his friends while the second is about dealing as much damage as possible to monsters.
Use inherent bonuses
One of the best rules options you can take advantage of is inherent bonuses. Found in Dungeon Master's Guide 2, p. 138. as well as the Dark Sun Campaign Guide Book, p. 209 (where it was expanded) inherent bonuses take the place of magic items for the purposes of system math. At set levels the characters will gain +1, +2 etc. to their to hit rolls, damage rolls, and their defense stats. Magic items are still compatible in that their properties, item attacks, and bonuses to crit damage remain, but their mathematical bonus does not stack with inherent bonuses. Whichever bonus is largest is used.
Focus on the story and the adventure, adjudicate their actions to fit
If you were playing 4e with adults I would wholly say to depend upon the use of the powers their characters have and play the system as-is. However this may be a difficult pill for your children to swallow all at once (there are plenty of adults on the internet that can't handle 4e's separation of fluff, the descriptions and lore, from crunch, the hard rules themselves). When your children's turns in combat come up or they are making decisions out of combat ask them what they want their character to do and then based on their answer formulate what their character would do mechanically and then walk them through what their character does. This way you can introduce and have them take over parts of the rules at 1 piece at a time.
To make your question short, and to see if I understood it correctly, we're talking about a player who made his character a certain one and roleplays it entirely different. You added that you think that it comes from inexperience, and that he created this character after you said "no" to some "freak-character"-ideas. You want to help him roleplay the character he created.
As I see it, this problem is made from two smaller ones. The first is that he doesn't see his character as interesting because the character "is normal and normal is boring". The second is that you wanna help him understand why the way he plays the character does not fit the story-world of your game.
Helping him understand that "normal is not boring
This is the more important problem, as it stands in the basis of the entire problem. If he'll see that normal characters can be interesting his "anti-persona" will perish and he'll roleplay a normal character and not a freak one. The main trick here is to show him that normal characters are not entirely normal, i.e. "no person is like the others". In order for that to work, we need to give the character depth.
The easiest way to give depth to a character is through internal conflicts. Having goals and all is nice, but without something that blocks oneself from achieving them it is far less interesting. First thing to do is to go over his character's background and see if he implemented there an internal conflict for his character. If so, show it to him and talk with him about it. If no, sit with him and help him to come with one. The internal conflict doesn't have to be extravagant, but it needs to be there. An example one might be that he loves Vincent's sister but secretly hates Vincent himself, or another like Loves the sister but thinks that he's not good enough for there. I'll take the second one as an example for this section.
The conflict gives us a few things, a few added benefits. It gives the character 2 conflicting goals: "Get the sister and prove that I'm worthy". Now, with those two we also get a kind of an achieving-plan: "If I'll show her that I'm worthy, by getting something amazing done, she'll want me and I'll be able to get her". More than that, the character gets the knowledge that each advancement in order to achieve one goal will drive the other one to the far end.
But the first conflict is even more interesting. The character here has the knowledge that he needs the brother in order to save his lover, but he just can't stand being near the brother. He'll drive the mission onward for two reasons but he'll have doubts about his lover- if he'll marry her he'll be stuck with this brother of hers.
To make long story short, simple conflicts can show the player that even normal characters are interesting and unique. When combined with goals they force the character to take certain steps along the roads, to commit certain actions along the way, that he won't want to do but will make him doubt himself and question himself and see that his problem are far more interesting than those of every freak that he'll encounter.
Another nice way to help him see the importance of conflict is through showing him and analyzing with him certain protagonists that are normal people, from the stories and movies and series (of any form)that he likes. He'll see quite quickly that the conflicts make them interesting.
But he may say that it is not enough. For that there are a few more literary tools that might help him see why normal people are interesting. The first one is having flaws (internal or external) and the second one is using "The Ghost".
Flawed characters are characters that just like normal people aren't perfect. Those flaws can be internal (self-doubts, for example, or a mild paranoia) or they can be external (they're look frightens ordinary people, for once, or a missing hand for the other). The idea is that the character has to deal with the flaw, and one day to find the strength to overcome it. The fight for the overcoming act makes the character far more interesting. A nice example of that can be seen in The Rain Man, where he learns at the end that he can count on strangers/"dumb" persons like he's brother. Another nice example can be seen in the story of The Ugly Duckling who although looking terrible learned to acknowledge himself and to accept the way he looks, to accept his difference.
"The Ghost" is an event from the past that just like a ghost haunts the character to this day. Again, trying to cope with it is what builds a deep character. One example for this can be seen in the movie Inception, where we literally have a ghost- Cob's wife. Another example for this can be seen in the movie Casablanca, where he has to deal with his broken relationship with Ilsa. This Ghost is far more interesting as the originator of the Ghost actually comes back to his life. In Frozen we see another kind of a Ghost- the act that one feels guilty about. Elsa actually killed her sister.
All of these techniques are there for one reason- to make regular people interesting, to give depth to the characters, to make them human beings with goals and drives and psychology.
Helping him see that his character doesn't fit the world
After he understands that he doesn't have to be a freak in order to be interesting, he will be far more understandable about playing a character that fits the world. Then, try to explain to him as calmly as you can what it is in the way he played his character that doesn’t fit the world.
Explain to him that the characters are in a world where being a freak is bad, where achieving one's goals is the ideal. Each and every one for himself, as the saying goes. Give him examples from the way he played his character and analyze with him, in a one-on-one conversation where his way of acting came from. Use the background he created to illustrate to him where your problem comes from.
Then ask him what problems he has with his character, and together try to find a solution. Maybe let him be just a little bit freakish. Maybe he needs to just create a different character. This is basically between you and him. After that show the updated character to the group and get their approval.
When combining those two, you'll get a player who his far more willing to both play the character while also seeing the problems with the way he played his character before.
Combining the two solutions
When combining the two solutions you get a better player, who understands for the future also how to create regular characters that are not freaks yet far more interesting than those freaks will ever be able to be. Furthermore, you get a player who is willing to play his character as written while still making the character fit into the world. Hope any of these helped you.
Best Answer
Facilitating Microscope can be hard because no-one is allowed to say “no” to a player during their turn but you still have to teach the limits that the game does need to enforce during a player's turn. The trick is to teach by example when you can (that's why the advice is to always take the first turn), and to pause the game for “teaching moments” without actually saying “no” so you can prompt the player to review the relevant rule and get some guidance on what the game needs at that moment.
Avoid vetoing — prompt them to think differently instead
For the specific example of making an Event-sounding Period, instead of “no”, prompt the player to just think bigger. They can have their Asteroid and Period too.
Say something like “A Period needs to be able to have many, many events in it. Think ‘the Civil War’ rather than ‘The Battle of Fort Sumter’. You can still say the Battle was the start of the War Period in its details.” Then ask them to think about what the larger Period around that asteroid impact would be, and make the Period about that. They can even still say (in the details) that a big asteroid impact defines the Period. (Later, that impact can be an Event itself to explore further!)
For an asteroid impact, this is actually pretty easy, because you just have to think about the surrounding circumstances and/or the fallout — like you did. You just have to make it a suggestion instead of a “no”. For example, either of these would be fine as Periods, and the player still gets to say an asteroid smacked into the planet:
There are lots of other variations that would be fine too. Ideally, let the player come up with the larger Period's idea rather than throwing suggestions at them. Evaluating your suggestions soaks up their attention, which can actually make it harder for them to sit back and come up with the Period. (Recall the game's advice here that it's OK and desireable to give the player whose turn it is quiet, mental space to come up with their turn's History addition.)
Facilitating Microscope always comes with a lot of tension, because as a fellow player you don't have the authority to say “no”, but as the facilitator you're trying to teach what the game is requiring of the players during their turn. So in general try to avoid saying “no”, and try to offer a vision of what would be more awesome, and then explain how that's more like what the game is asking them to do.
A side problem: Avoiding sounding like “the GM”
One knock-on problem I find is the need to avoid giving the impression that the players need my permission during their turn; this is intensified by the fact that they're used to me being the GM in more traditional RPGs we play. To combat that, while also attempting to facilitate and guide the players into Microscope's rules, is to emphasise repeatedly that they have ultimate autonomy during their turn, so long as they don't contradict the established History. Laying this foundation makes it easier to avoid that impression when I have to correct someone on the rules during their turn. It also makes its easier for me to think in terms of soft guidance, rather than “no” or vetoing, in the way that I phrase any game-pausing explanations I end up making during a player's turn.
If all fails, it's OK to let a too-small Period happen
And, in the end, it's not that bad for the game if one Period ends up being a bit too much like an Event. The problem that causes may not even come up, if it's not “big enough” to attract other players' attention and attempts to create within it. And if people do build within it, the cramped nature of an Event-like Period will become more obvious, and a teachable moment.
This fact that it's not a huge problem to allow the cramped Period gives you more leeway to let it slide if your advice is too soft to fix it, or if the player insists on making it anyway. You can advise, and just let it happen if the advice doesn't stick. You can always come back to it after the game, since everyone will understand the issue better after having played the game through once.