Having lived through a similar situation, my main advice would be, very strongly, don't let yourself get rushed and railroaded.
In ordinary, calm circumstances, there are just so many , many decisions to be made.
In these stressed circumstances, it's even harder.
Just say no, I'm not ready, I don't want to mess your around, so I simply have to take the time to be sure of my choices. So they get held up? So what? Any inconvenience to them is trivial compared to what your family is living through.
As you said, specify paint type: no need to choose colours at this point.
It's best to be sure about things that are harder to change later - electric sockets, and where the lights go. Don't assume that because it's still visible in a water damaged room where the sockets are, that they will get put back in the same place.
You will, I'm afraid, need to carve out chunks of time, every few days, to check on what they're doing, and compile an ongoing snag list.And insist it gets done to the standard it was before.
I would caution against your loss adjuster handing the whole project to a company that specialises in insurance renovations. These guys never have to get work from the public, and they never have to work for anyone twice. Long as they're cosy with the loss adjuster, they'll get lots of work. So they have no reputation to uphold. And they can be very crap indeed. Choose to use builders and professionals you've used before, or who come multiply recommended. And someone who regards YOU as a client to be pleased, not just someone working for the insurers, who couldn't give a darn if you're happy or not.
Once the specs been drawn up, and priced item by item, you should be able to negotiate changes - for example, if you can add money, you can go for a more expensive finish. Or if they've itemised £X 00 for flooring, if you can go round suppliers, and source flooring , in a sale or end of line, for £X minus 30 %, then you could put that money saved towards eg a more expensive bath.
Again, time consuming, but may be worth it.
And insist on eyeballing everything that's put in - oh yes, we'll get a absolutely same quality kitchen for you, yeah insist on seeing it , and checking it out for yourself.
Sorry if this all sounds negative. I've met one person who was delighted, and found it a smooth process. But, sadly, several like me, who found it stressful, and needed to be assertive.
The good thing for children, is the message that bad things can happen, and can be sorted out again. That's not a bad thing to learn young.
I was so glad that it taught me what was important: we walked away in the clothes we stood up in, but we all walked away.So didn't lose anything important.