This is for family. Demanding a contract seems incredibly ill-advised especially as, I am sure, the OP's parents played a large part in getting the OP to actually agree.
Many of us have been in the same boat. Family pressure can be a very powerful force. Learn from this experience and, the next time you're asked, you'll be better prepared for polite but forceful refusal.
I assume this is in the US, so asking for a contract in family affairs is not so far-fetched if TV is to be believed