Do you have the option of letting your own insurance handle the claim and then having them deal with the other insurance company? That's how I handled it when my truck was damaged. The other person's insurance was stalling me so I called my own insurance company. They made an appointment for the same day to get my truck repaired and paid everything above the deductible. Once the claim was settled they reimbursed me the deductible I had already paid.
Laws vary by State and it sounds like you have the additional complication of dealing with two different countries.
I wish you the best and agree with ij2654 that you should probably be talking to a lawyer. It sounds like you're going to get shafted if you don't.