Thanks for all the suggestions.
I think there are two scenarios, the first being before ds passes his test and the second being after.
At the moment, dsd has unlimited use except for each Saturday afternoon and (generally) a weds night which means she's very used to having the car. She doesnt infringe on ds time but it's so limited right now, she's not really being impacted on. Dsd learnt on a Saturday with the same instructor, so we are doing the same for ds. Ds does a long school day, so don't really think it's as good to swap to a weekday for lessons as he'd be getting less practice than dsd had, which doesn't seem fair and frees up the car for dsd to use all weekend every weekend.
Of course we knew there would be issues and compromises to be made, it would be hard enough with two teens without adding in the blended family dynamics.
If we leave them to sort it out themselves, I suspect dsd will be more organised and just book the car all the time. When ds does think about going out, he'll just realise that dsd has it booked so will just shrug his shoulders and not go out. There's distinct differences in personality in this way. I'd like to think he might become more organised but I know he won't!
We had said they could use it one week on and one week off for getting to and from school once they both pass but in the meantime she will have it every week.
I'm really aware it's not her fault her mum won't help her out, but it's also not our fault or ds fault either. She has a full brother who doesn't see us, so going to mums is the time she sees him. So it's impacting on him too if dsd stops going.
I think we are going to have to do a one week on and one week off rota once ds passes with maybe exceptions for important events (of course, dsd sees all her socialising as important!).
Both dp and I see ds using the car to learn as v important particularly as dsd has already had that privilege. So that needs to stay.
The reason she wants the car this weekend is to go to a friends and watch dvd's and chauffeur a load of friends there. Maybe that shouldn't be a priority?
To whoever said about our choice to live rurally, without giving too much away, dp has a career that can only be done rurally. We certainly wouldn't be an a position to fund a car if he was t working rurally.
We are both prepared to give lifts to either of them if the other has the car, but of course, this isn't fair on dsd if she's at mums because no one there will help her.
The other issue is mum asking her for lifts when the car is at mums and dsd paying for it. Yes, this has already happened.
I'm considering telling her if she wants the car, she has to stay at ours but ultimately that just gives her a free reign on the car whilst going to mums could be used as a way of getting her to actually go without the "shared" car sometimes.
I don't think there's an easy solution and I also think I'm a bit scared of upsetting dsd as she's not mine, there's always that extra layer that goes with step situations.