Ah, teenagers.
I'd reiterate the original deal was that you would match what she gave you here and there and that it was for college/car.
This account was between the two of you, not you and her mom. If she doesn't want to handle the account with you, then that's fine, but that's her choice. If she doesn't give you the money, then it doesn't get matched. Also, $100 here and there doesn't mean "give me three paychecks and I'll match them." If you still want to match, then match as you can and remind her that you can't financially swing all that money at once. Her failure to put money aside little by little doesn't constitute an emergency now on your part.
Now, you can either decide to do this even though her mom is buying a car and consider it "college money", or you can say that since her mom is buying the car for her, the original purpose of the account is void.
My husband has a joint account with my stepson so he can give stepson money for books, pizza, etc. Stepson knows that he isn't to come to us asking for shampoo or laundry detergent. He's 19 now and should buy his own. That's why his father gives him a bit of money. This account with your stepdaughter could be like that - a little extra for the little extras.
Remember, ultimately it's up to you. You aren't legally obligated to make up for her parents. You're just being really nice, and if she doesn't appreciate it, you don't have to do it. And I'd limit it. I wouldn't go on and on indefinitely because she IS earning her own money and will be getting a car from her mother. Don't be the Bank Of Stepmom, especially if she's disrespectful to you. Don't let her take advantage.