You are being understanding enough to allow her to move in.
I have a grown stepson living with us and I also have a small daughter. I understand what you are dealing with.
What you need to do is talk to your DH. You can say, "I appreciate and understand that you want to save SD. But she's 20 years old and she's already proven that she can't handle things that are just given to her. I will agree to have her living in our home but there have to be conditions. Not just for her but for the sake of everyone else. We are not a bank and we have 3 smaller children to care for. This is about limited resources and we must prioritize them. If she moves in to save money, then she can buy her own car."
What my DH sometimes sees my reaction as is "she doesn't like my bay-beees" when the truth is I just see that they are NOT babies and can fend for themselves. Right now my SS is close to having $5K in the bank. Please do not look at my bank account, as I had to pull from another savings account to pay my bills last month. So the way I see it, if he can save $5K, he can move out in the next 6 mo. or less. He is not helpless. Heck, he can buy ALL his own groceries, but that is not a fight I won. I did get DH to agree to charge minimal rent.
I would keep talking to him in real budget terms. Lay out the budget. You need x for the movers and x for this and x for that. There is no money for a "want" like a car for SD.
Last year, my DH and I got into a disagreement because he wanted to buy both sks cars. Turned out, he couldn't do it. He had promised me that DD would be able to attend preschool and after looking around and realizing that "cheap" cars were not so cheap, he only got SS a car. SD doesn't truly need one for her campus job. I put my foot down. He was NOT going to sacrifice our baby girl's schooling for a car. A car is a "nice to have" - and also comes with care and feeding requirements. If she won't pay for her own insurance, gas, or maintenance, then it becomes your burden. If you wouldn't buy a new car for YOURSELVES then she doesn't get one.
Ask him why he feels he has to buy her these things and why it is more important to buy them than to encourage her to be independent? The answer may be telling.
The answer may also tell you that she shouldn't move in and/or you need to consider family therapy.
There are books out there that call this "emerging adulthood" and equate it to adolescence. I call it "excuses not to get out of the house and act like an adult."
ETA:
IMO, "taking on responsibility for" your stepchild doesn't = being a doormat or a blank check. Where is her mother? Can't she cough up something for the car instead? I sometimes have to remind my DH that even if BM is lazy on the follow through/support, she exists and can be another resource for HER children. I signed up to be a stepmother. I did not sign up to be an indefinite provider for two grown people. Even my own little DD will be shooed out of the nest when it's her turn.
If she currently can't even drive, then that needs to be priority. My sks both had to take driver's ed that we paid for (mandatory to take a class). Buying a car when she can't drive it is cart before horse stuff.
And having your parents buy you a car, pay for your food, let you live in their house, pay for college - they are all NICE TO HAVES when you are an adult. I bought my OWN first car and paid my OWN way through college. Even if you were her mother, no prefix, you do not "owe" her anything like a car, especially under these circumstances. It's not about her being a stepdaughter. It's about her being an entitled brat.