I'm Lucy, and I'd be happy to answer your questions today. I'm sorry to hear about your dilemma.
The contractor should split the estimate into materials and labor if you ask, and if he won't, you can hire another company (as long as you haven't signed a contract yet). Until a contract is signed, you can negotiate a clause that puts a maximum on the amount they are allowed to charge without confirming with you IN WRITING. That's unfortunately only possible before you sign a contract - they wouldn't have to agree to do that after. Everything in a contract is negotiable until it's signed. You should be able to tell them you want to buy the flooring yourself and just have them install it, and they can put that in the contract, too.
The construction company can't refuse to do any work that you hired them to do. If you have an agreement that says they'll install the floors, and they don't do it, you'd be allowed to sue them for the cost of having someone else do it. And keep in mind that even if the insurance company sends you a check for the value of the estimate, they don't get one lump sum payment. Typically the contractor gets a portion of the payment first, to buy materials, and the rest is due when they're done.
If you have any questions or concerns about what I've written, please reply so that I may address them. If I did not address the specific thing that you wanted to know, it may not have come across clearly to me, so please restate that question. It's important to me that you are 100% satisfied with the service I provide. Otherwise, please rate my service positively so that I get credit for answering your question. Thank you.