During the playtest, there was a Charge action that all characters could use. What it allowed was that as an action, you could move up to half your speed, and attack any adjacent creature when you finished moving. This effectivley allowed you to have a movement of 1.5 times your normal movement rate, in exchange for losing extra attack etc.

Besides trying to figure out what half of 25" is, and being open to the odd debate about if it counted as an attack action for extra attack or not, it didn't negatively impact our game much. We did not add any bonus to hit, or a penalty to AC, but if worrying about those modifiers is not a concern, or if you enjoy that sort of thing, I think a +1 in either direction would be fine.

Compared to the feat, there is still a reason to take the feat since you gain an extra 10-15 feet of movement, and can also shove and not only attack. However, I would bump up the feat to also give a +1 to str to compensate for the new houserule.

TL;DR

1. You can use a reaction on your own turn
2. The charge is not interrupted
3. The charging creature gains no bonus on the opportunity attack

Details...

So, to clarify the scenario, we have three creatures. I'll give them names:

• Bob, the charger
• Jane, the target of the charge
• Nelly, with the readied action to move

Bob charges, Jane. But Nelly has readied an action to move. As soon as Nelly sees Bob, she wants to run across his path directly in front of him. What happens?

First, a "charge" is not a discrete action. The Charger feat, PHB p. 165, says:

When you use your action to Dash, you can use a bonus action to make one melee weapon attack or to shove a creature.

If you move at least 10 feet in a straight line immediately before taking this bonus action, you either gain a +5 bonus to the attack’s damage roll (if you chose to make a melee attack and hit) or push the target up to 10 feet away from you (if you chose to shove and you succeed).

So Bob has taken the Dash action. Normally, Bob would attack Jane using a bonus action after finishing his move.

However, in this case, as soon as Nelly sees Bob, she interrupts Bob's move:

Page 193, PHB:

Ready

When the trigger occurs, you can either take your reaction right after the trigger finishes or ignore the trigger.

So, in this case, the "trigger" was "as soon as Nelly sees Bob". So, she moves, crossing his path directly in front of him, and provokes an attack of opportunity in the process.

Nelly, is the one moving at this point, so only Bob gets an attack of opportunity, not Nelly.

Even though it is Bob's turn, he can still take his reaction to make an opportunity attack, p. 190 of the Player's Handbook:

Reactions

Certain special abilities, spells, and situations allow you to take a special action called a reaction. A reaction is an instant response to a trigger of some kind, which can occur on your turn or on someone else’s.

The charge feat allows Bob to make an attack as a bonus action, and possibly gain a bonus to that attack. It does not grant a bonus to any other actions, or attacks. So, Bob does not get a bonus to his opportunity attack.

From the Charger feat:

If you move at least 10 feet in a straight line immediately before taking this bonus action, you ... gain a +5 bonus to the attack’s damage roll

Next, after Bob makes the opportunity attack, Nelly completes her movement, and Bob's turn resumes.

Bob may continue his movement toward Jane, and use his bonus action to make an attack as granted by the Charger feat.