Four lesser options, one major one.

1. Fast-forward the split party part. Don't dwell on stuff as much as you otherwise would.

2. Snack and bathroom break time. Shoo the other players off. This will serve as a cue to the sneakers that they should include everyone eventually.

3. Metagame, encourage the group to find ways to include people even when it's suboptimal.

4. Spring stuff on the other party to keep them occupied. Sure, if they just get a lead, they can wait to follow up, so make the action come to the PCs - someone kicks down the door or otherwise looks to interact with them NOW.

5. Give them all equal spotlight time. 5 minutes dealing with sneakers or interrogators, 5 with the others. They'll either start going to do stuff of their own accord, or they will, heaven forfend, roleplay with each other.

Number 5 is really my favorite. We've had plenty of great moments while half the party is doing something "important" and the other half goes to a bar and gets in trouble. All you have to do is give them the spotlight time, PCs are notoriously twitchy and impatient and will find ways to entertain themselves, "on task" or not.

My added thoughts based on your question edit.

You don't need to balance "in game" time. If one group went and did something for six hours, but real time that took five minutes, then you just need five minutes of spotlight time for the other group, even if that's five minutes of rousting a hobo and then 5:55 of "we go somewhere and hang out."

If they need ideas for what to do or you want to spring things on them - that's why God created random encounters, right? Either they self-motivate some mission oriented stuff, which you come up with, or they mess around in a tavern or go shopping, which you come up with, or they sit around looking glum till a land shark attacks them, which you come up with. You do anything you'd normally do to the full party, but ideally with slightly less kill. (Or not, if you want to dissuade them from splitting in the future.)

If they are content to wait in the bar, let them wait in the bar. Have fun bar things happen. People hang out in bars in real life, it's fun. And sometimes good and/or bad things happen, hence the larger than usual incidence of hookups and cop interventions in bars. All you need is for them to all be having fun and getting roughly equal "spotlight time" (time they get to actually do something at the game table).

Not everything has to be mission related or be a "subplot." They can just find out interesting things about the world they're in. If every story everyone ever tells them is a "subplot," then you get into a bad rut where their expectation is that anything that happens in the game world is FRAUGHT WITH MEANING, and it can't just be some guy BSing about how he fought a troll armed with a spoon once.

In my campaign, I make sure there's a healthy amount of "the world doesn't revolve around the PCs" stuff going on. Not only does it make for a realistic feel, but then when someone wants something to do, they have the expectation that "Hey, I can just go out there and go shopping, or find a bar, or find something to do - I don't have to be 'working through a plot element'" every damn minute of every damn day.

In my Pathfinder campaign recently, the party split. One half was going to do something on task and important. I don't even remember what it was and they probably don't either. The plan was to meet up at a known bar later that day. The other half of the party decided "we'll just go wait at the bar now." I roll a random encounter - giant cockroaches. They get to the bar, and the owner, "Ball-less Bill," an old ex-pirate with one leg, one hand, one eye, and apparently less then one thing down below, was standing outside the bar holding the door shut. "What's the problem?" "My basement flooded and there's these big ol' cockroaches running around in there! They're as big as dogs!" "We can take care of this! Stand aside, Bill!" The two PCs bust in and the cleric casts Call Lightning. The cockroaches are like CR 1/4, so they run all around and out into the street as the cleric blasts lightning holes in everything in sight. The fear of God is put into the local yokels, and the cleric gets an Infamy Point (the equivalent of a Hero Point in my pirate-oriented campaign). They yell "Wooo!" and go in and drink for free.

The other half of the party... They did something on mission. Got some information or something. Who cares. No one remembers that, but they remember the Great Roach Holocaust.

If you have proactive players, this shouldn't be a problem. If you have reactive players, then don't treat them like proactive players and give them 'things to follow up on.' Have the world turn, and its events happen around or to the players. If they decide to just go find another bar rather than chase out the giant cockroaches, fine, then make them choose whether they're drinking "bloodwine or dwarven grog" and go back to team A. Seems to me like you're overthinking this by requiring all events to be part of some big Mythic Plotweb.

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.