You are quoting expected CR - the final CR is much higher.

On base hp 178 × 1.5 for immunities gives 262 - so defensive CR 13. Expected AC is 18, so an AC of 16 gives no adjustment.

Expected damage per round (~45-55) from its breath weapons (3 with a 1/3 recharge chance - it will have one every round) plus some acid blood splash against 1 PC - assume it can hit 2, so 90-110 or Offensive CR 16. This is an "effects" monster so any adjustment to this should be on its save DC which is 16 instead of the recommended 18 so no change there.

Averaging and rounding up gives a CR 15.

In practice there is no good way to force them together. A little bit of it can help a little bit, but it only helps a little bit… and the more forcing you do, the less effective it becomes as the players fight the imposed action.

Even if you successfully regroup them, players are nothing if not unpredictable. As soon as you manage to get them together again, they're likely to figure out how to safely (or at least, so they think) split up again. After all, they have pressing business elsewhere!

So the trouble with forcing is that you end up taking away everyone's turn. Your players are putting up with the delays and turn-taking because it's actually better than the alternative.

(Never mind the problems that throwing something adversarial in just to shake things up can cause. In one game I was part of, the players were enjoying their different pursuits, and then the DM threw in a “oh no someone stabbed the bartender and now there are extortionist gangsters” thing, because he thought we were bored. It ended up actually killing off the campaign because we weren't interested, it squashed the fun RPing we were doing, and we couldn't get away from this uninteresting plot thread.)

Better even than forcing is giving occasional opportunities for the party to regroup, but don't arrange them so that they're obviously mandatory. “Hey fighter, the magic sword auction doesn't start until this evening. Unless you have any other business, might be good meet the party back at the inn to see what they think about your discovery.” But this only goes so far, so it's nice but it's not going to feel like it solves much.

The actual solution

Keep doing what you're doing! But recognise that managing spotlight time is a skill, and you only get better with practice.

What I've learned is that switching more often between different groups is effective at keeping everyone engaged.

But that brings the challenge of doing it smoothly and at the right time. There's no secret to picking good switching moments — that's where the skill comes in, and the practice it needs. You try, and you watch your own GMing patterns and practices, and you look for where you did well and where could have done better. You learn from the mistakes and from the successes, and you get more comfortable playing the Time Conductor who's flipping from scene to scene to keep the spotlight moving and focused on interesting things.

There is one small trick that I've learned though: there are many times where what you present to the players requires a bit of thought from them to figure out what they want to do. When you hit one of those moments, you'll ask “what do you do?” and the player will be unsure and play will stall. Normally in a full-party scene this is when the GM just sits back and lets the party chew, but when you have a split party this is an opportunity for a spotlight shift. “Cool, think about that and we'll come back to this in a minute. Meanwhile Wizardpants is at the School of Arcaneyness and…”

So to sum:

• Present opportunities for the group to get back together, but don't force it. And don't force yourself either — do this when it makes sense and you have a good idea, not because you're desperate to simplify the situation.
• Keep moving the spotlight around like you're doing.
• Be patient with yourself. This is a skill that improves with use.
• Learn to spot more kinds of opportunities to switch smoothly.
• Treat player indecision as a gift that gives you a natural switch point.