The specification:
Starting at 3rd level, you can use a bonus action to make a Perception check to spot a hidden creature or object or to make an Investigation check to uncover or decipher clues.
Suggests that a bonus action specifically will be useful - meaning that the Investigation check will be useful in a combat or other time-crunch scenario.
Uses for Investigation checks
Taking some examples from the DMG on how an Intelligence (Investigation) check might be used in combat:
Perhaps your party is being chased by a powerful adversary, and you need to escape a dead-end room. DMG 104:
Opening a Secret Door. Once a secret door is
detected, a successful Intelligence (Investigation) check
might be required to determine how to open it if the
opening mechanism isn't obvious.
Perhaps your party is engaging an enemy in a battlefield that the enemy had the chance to prepare. Detecting and disabling the traps for yourself or your allies is key. DMG 121:
If the adventurers detect a trap before
triggering it, they might be able to disarm it, either
permanently or long enough to move past it. You might
call for an Intelligence (Investigation) check for a
character to deduce what needs to be done, followed
by a Dexterity check using thieves' tools to perform the
necessary sabotage.
There's plenty more ways, depending on how combat goes. You might need to quickly figure out how to use the MacGuffin to annihilate the baddy, or spot a clue as to their social ties that you can use for leverage.
Balance
The Swashbuckling Rogue Rakish Audacity feature:
[...]
You also gain an additional way to use your Sneak Attack; you don't need advantage on the attack roll to use your Sneak Attack against a creature if you are within 5 feet of it, no other creatures are within 5 feet of you, and you don't have disadvantage on the attack roll. All the other rules for Sneak Attack still apply to you.
Only really works for one-on-one fighting, you can have neither allies on your side, nor additional enemies. While it is certainly powerful, it's not quite an always-free Sneak Attack.
And the Panache feature:
[...] If you succeed on the check and the creature is hostile to you, it has disadvantage on attack rolls against targets other than you and can't make opportunity attacks against targets other than you. This effect lasts for 1 minute, until one of your companions attacks the target or affects it with a spell, or until you and the target are more than 60 feet apart. [...]
This feature occupies a different niche than the Inquisitive Insightful Fighting feature. Panache is more of a support feature, making the enemy less likely to hit your allies, while Insightful Fighting helps you deal damage directly. The value this brings to you depends on your team composition and tactics.
However, you're right in that the Inquisitive subclass is altogether weaker directly as compared to the Swashbuckling subclass. Initiative and Attacks of Opportunity are all things that take part in every combat, whereas having the combat depend on your character quickly identifying some tipping point is a lot more circumstantial. If you want your Inquisitive Rogue to use their class features in combat more, and in a meaningful way, you should talk to your DM about it. The examples above show that there are ways to make Investigation useful in combat, it then falls on your DM to give you these opportunities.
There is a mechanic that you could adapt from Blades in the Dark (at least, I think it was Blades in the Dark, it's been a while). Basically, instead of asking everybody to run Athletics and be done with it, you tell them that they need to achieve a given amount successes in order to escape. The way they achieve them is totally up to the players, but they can't just mindlessly repeat the same action, they need to try different things each time.
For instance, you could tell a group running away from a monster that the monster is really on their heels and they need four successes to escape. You can even draw four squares on a bit of paper and check one off every time they achieve a success.
Probably they are going to start by trying to outrun the monster, they might roll athletics and succeed, then you check one square off and say "alright, you've put some distance between you and the monster, but it's still running after you, what do you want to try now?" Now they might try to hide from the monster, set it on a false trail, or disguise themselves to scary it off. The more things they try, the more crazy ideas they are going to come up with, and you can always ask them to narrate each action if you want some more juice (if they say that they try to appear scary to scare off the monster, ask them to describe how they are doing it, not only roll dice).
This mechanic can, of course, be used for any other kind of challenges, not only running away from scary creatures.
To make it more interesting, a critical success can count for two and a critical failure can set the party one success back.
Active opposition
There are at least three ways you can go if you want to add active opposition to this mechanic.
Add a challenge for the opposition. The opposition needs to achieve a given amount of successes, like the party. It can be the same or a different amount, but keep track of it separately from the party's. Whoever achieves all the required successes first, wins the challenge. This works better if both sides are trying to achieve the same goal, like a race or an athletic competition.
Make the opposition set the players back. The opposition might do some actions that, if they succeed, add one more success to the amount required by the players. For instance, in the running away example, the monster might trigger an avalanche to cut the player's escape route. Then you would draw one more square in the paper with the amount of successes required for the challenge.
Add a time limit. If the party don't overcome them in a given amount of rounds, the opposition wins. The opposition is not really actively preventing the party, but the end result is not too different.
If I recall correctly, the first one is in the rules for Blades in the Dark, but the second one isn't, because the system puts a strong focus on the players driving the action. If you want to use the second option, I recommend to do so sparsely, and in any case I wouldn't make the opposition make actions that may set back the players more than once or twice for challenges that are not already difficult.
Best Answer
To answer your two questions in backwards order, but easier context:
Scene Framing
Splitting the party is easy and fun when you don't let scenes drag. Just as much as movies and TV cuts to relevant points, you should aim to start scenes as close to the important action as possible. Don't spend long on the set up, get to the interesting point of the scene ASAP. Throw clues in their faces. Put hard choices there too. And, cut away quickly too. Scenes should be 5-10 minutes at most. Since we're not talking high crunchy combat scenes, cutting away is very easy to to do here.
Known, Sought, Given Information
So, you're doing an investigation adventure, right? Go watch some investigation shows, read a few books. What happens in these stories? There is NO WAY for the protagonist to NEVER get the clues, it's really only a question of how they get the clues, how beat up they get along the way, and whether the clues come in time to do something about it or not. (Usual Suspects is a great movie example of getting all the clues too late.)
Information comes in 3 ways:
Known
Known information deals with things the characters ALREADY know. This can be inferred from their skills, their classes, backgrounds, history, etc. "You were a galley slave before being a pirate, you recognize the scars on the ankles from chains anywhere..."
Use this give each character plenty of context, plenty of "read" on characters or objects. ("He walks with a swagger, not the kind that comes with hardship, the kind that comes with having lived one's entire life at the top. You can see the difference anywhere. He's not one of you.")
Known information should often include lots of free clues or reads on things, because it gives players a feeling of expertise and competency for the characters. You can have dice rolls or whatever about specific questions or further clues, but start with the info their character can JUST SEE from the start.
Sought
Sought information has to be... sought out. This means it's not immediately obvious and either has to be collected ("pickpocket the letter tube from his bag"), or "processed" in some manner ("Scraping the iron shows it to be a softer type than normal. This was a cheap replacement, not the original.").
This is where character skills and player choices can be made, but since few players think of their characters as investigative types, you will want to provide some suggestions along the way. ("You've traveled far from home, but you're the best one on the ship when it comes to recognizing foreign plants. Maybe if you got a look into the doctor's herb bag you'd know what's in there...")
Also recognize that while a social character can con, trick, pressure characters into revealing information, the quiet high-perception character can often read other things about someone without directly interacting with them. Consider that a potential parallel method as well.
My suggestion is that if you have any kind of sought information available, make it something the players acquire/understand with just one skill check/dice roll/etc. Failure shouldn't mean "you don't learn anything" but it might mean "You get caught trying to get this", "The evidence gets destroyed/lost", "You only figure out what it means too late" etc.
Given
Here's a thing few rpgs get from investigative stories - a lot of clues just FALL into the protagonists' laps. People spill the beans, come forward, tell the dirt on someone else to get them in trouble, the heroes just happen to luckily be at the right place to overhear some incriminating statements, they stumble upon a crucial clue left forgotten at a crime scene... this stuff happens a lot. The only reason other media gets away with it is that the heroes often suffer so much it's like "well, sometimes you gotta get lucky, right?".
One of the better rpgs to deal with investigation is Dogs in the Vineyard, which has a pretty simple bit of advice - have several characters try to GIVE the information straight to the PCs... lying or omitting just enough to cover their own asses or their friends. The other bit of advice is that straight out lying should have the GM say to the players, "You can tell they're lying, you're just not sure what the real truth is."
AS long as everyone is at least looking for information, one of these three types should be available to give clues or at least ideas on how the characters treat/feel about each other.