My dd wasn’t quite in the same league but she went through a similar phase. A tip I had was to bookmark cuddles, basically giving them a clear beginning and ending
eg “I’ll give you a hug just as soon as I dry my wet hands”— or “let’s sit on the sofa over here and have a cuddle” so that there is a slight delay beforehand
Then point to the ending before it happens
“We’ll hug for another minute and then I have to finish those dishes and you can come and tell me all about school today” with an extra big squeeze at the end.
It’s not that it worked magically to satiate her (far from it) but it helped me a bit. I knew I was giving her quality attention at times (because I was saying it) and it got me over the feeling of being half hearted all the time.
And it helped us find substitutes - cuddle me from behind/ hold this for me/ cuddle teddy while you’re waiting for me.
And helped me uphold boundaries which are important. In the car example, would you end up holding her hand while driving? That’s obviously a big no, and I’ve probably misunderstood but I found it helpful to have a few hard NOs that she couldn’t push me past, for her sake really.
Another tip was hugging her a little longer than she wanted, so that she was the one squirming away sometimes.
It’s hard. It passes eventually.