Do you think I should tell my parents about a lady who tried to drive me home?
What about the situation with her was concerning to you?
She was drunk, and a stranger. She shouldn't have been driving or offering rides.
It is unwise to ever get in a car with someone you don't know. It is even more foolish to accept a ride from a drunk person, so it would be wise for you to tell your parents about the situation.
Do you think they'll be mad?
They won't be mad because you didn't accept the ride from her, and you told them about it. I think they'll be proud of you for having good judgement and not getting in her car.