What do you do when the at-fault vehicle's insurance will not pay you for your totaled vehicle because the insurance company has already paid for other vehicles damaged in an accident?

Based on your question, I'm guessing that their policyholder simply didn't have enough coverage to pay for all the damage to all the vehicles involved. I would have to know a little bit more about what happened, but you're only realistic action at this point is taking their policyholder to small claims court.

However, if you have your own coverage, use it and let your insurance company deal with it.