Your daughter sounds selfish to me, what you're asking for is a very basic level of filial reciprocity. I know the UK doesn't encourage this, but I think what you're asking for is extremely reasonable.
Getting a whole new car bought for you isn't a small thing. And she can't even be arsed to give her mum the occasional lift here and there? Out of basic love and concern and yes gratitude, if nothing else.
She's got a good deal. Does she pay rent? Bills? How much does she contribute overall?
I don't drive either OP I've never wanted to, but the suggestion up thread to learn might not be a bad idea. You might try a few lessons, you don't have to put pressure on yourself about taking tests or anything. Take a few lessons and see if it's something you want to pursue. You could then potentially share the car (not that that might go down well)
I'm suggesting it because sadly, your daughter does not seem like the type who is going to be there in a significant way should you get ill or anything.
I personally would have it out with her, and I wouldn't care about any fallout. I know new boyfriends can be distracting, but family is important too. That said, do not criticise her spending time with her BF. But do express your disappointment of her overlooking to support you in what are fairly average expectations of help.