On parent support for the small sedan. You didn't mention what amount of money the parents were contributing to the daughter's car purchase, 0%, 50%; 75%? If the kids pooling their money means that parent funds for the project are 0% then you have to step aside and let her purchase the car. "Veto" power is what you've exercised at the moment and that is not going to win a popularity contest. Explain to your daughter you love her, want to see her reach her 25th birthday, want her to be safe. If you are putting money into this project then you can veto it, but it won't be popular.
As for a vehicle for teens. Nothing is perfectly safe, since we are talking about teen drivers. Best choices are mid sized sedans with safety features found on new cars and that makes it expensive. Since teens have little money older cars, smaller cars, and probably less safe cars are common. A Chevy Tracker is OK in a lot of respects. Its not a fast car, and excessive speed is the biggest issue with teens. It is "tippy" like all SUV's but it isn't as big and prone to tip over as many bigger SUV's. The tracker is not likely to have too many passengers since the rear seat is very cramped. I'd rather see my new driver in a Tracker, than a Mustang, or a hopped up Civic.
Whatever car see gets SHE is the biggest safety issue. We told our son (driving since Aug. 08) that if he took more than one passenger he'd lose the car for a day, 2nd offense 5 days, 3rd offense 10 days, etc. Same if we saw him driving recklessly, like speeding on our neighborhood streets. So far only one offense, and he got the message we were serious. Set the rules and you and your husband need to line up on them and enforce them.
Sharing a car between siblings is a matter for them to decide and work out. Lots of problems but it can be done. It is an area you need to stay TOTALLY out of. Don't get in the middle or try to act as referee on this. Have them make up a contract between themselves that you can act as a consultant. It should have a buyout provision when one person says they want to own the car individually how will the other be compensated. It should also how the costs of insurance, repairs, and maintenance are to be shared. The first time a dispute comes up you'll wish you had a contract. This a good opportunity for young people to learn about the responsibilities of owning a car, it isn't always fun.
As a parent my concern is safety. I'd pony up for repairs of safety items, such as tires, brakes, and repairs that were safety issues with the cars. Gas, oil changes, were the kids responsibility. This system kept the relatively older cars they were driving as safe and maintained as possible. If she is driving a Tracker, with good tires and good brakes you can be a bit less nervous.
At 20 years old you have to get OK with being uncomfortable about you daughter's safety. Her safety is becoming more of her responsibility for herself. If you have done your job teaching her how to be safe and responsible you've in the watch and see how it turns out stage. It is time to step back a bit, let her test her wings as she prepares to leave the nest.