[RPG] How fast does fire spread

Don't make it your problem.

Make it their problem. (The players).

If you don't want to run a split party, since it increases DM work load, then before the next game session begins you need to tell the players that you are not interested in running two games instead of one.

Core reason: DM's are allowed to have fun too.

Then, as you suggested yourself, set it up so that they come across each other.

Then let them role play the outcome. It may be resolved that they will never work together: not your issue, theirs. If that is how it works out, do as @Dan B suggests and have the loner become an NPC, roll up another PC.

If they work out a compromise, good. They have solved the problem, you haven't had to.

Here's the tricky part: they accuse you of railroading. Your response: I am not interested in running parallel games. We go back to DM's get to have fun too.

Since there are only three of them, it is to their advantage to hang together in a team based adventure game like D&D 5e. You should probably point that out as well.

If, on the other hand, you don't mind running parallel adventures, then there isn't a problem. Just do that, and do your best to share DM time as 2/3 to 1/3 (The player who splits off gets 1/3 of your time not half. Thanks to @Greenstone Walker for that recommended split in DM effort). The reason I provided the answer is that it appears that you do not wish to run parallel adventures.

In response to your sectionals:

• Slowing the game down:

Do NOT repeat things for them. If they miss it, they miss it, they have earned no special treatment - do not offer them any. As much as I personally dislike it, a time limit (say 1 min) for each player, each turn may be in order. (the time limit is only on committing to an action, not actually finishing it ... ie large meteor swarm could take a while to resolve)

• Losing a sense of cohesion:

If their characters are no longer fulfilling a prerequisite for something, then their characters should suffer some penalty or issue. This is an item for the DM to discuss with them. Although it could lead to booting the characters (not players) from the party, it could lead to new character creation .. or even player dismissal ... although this isn't necessarily what I'm leading at here ;)

• Ruining Immersion:

If the players themselves are not abiding by the rules of the table, and communicating with them has failed, I'm not sure I see any other option than to start enforcing stricter penalties on them, or asking them outright to leave. I know you didn't want to hear that, however, some people just don't "get it". shrug

• Poor Gameplay:

You don't need to handle this behaviour, neither does the GM. Just simply point out . "Hey, it was your choice ... live with YOUR choices". These hard heads need to grow up .. short and simple. :)