My mother was involved in a car accident on the highway in Houston,Texas in which she was at fault.
She rear-ended a truck and both parties agreed on location to not file a report or call anyone and just work it out within the parties. The person she hit is now calling claiming vehicle damages in the Thousands of dollars, we feel this is excessive. Does my mother have any legal obligation to comply with these demands?
Your mother does not have to pay any money until a court says she must.
However she should review her insurance policy which tells her what to do in the event of an accident.