Your take is one possible explanation.

Another is that she's trying to be considerate. Because maintenance is his profession, maybe she wants him to have a break from that kind of thing when he's with her. She doesn't want to be seen as an extension of his working hours. She doesn't want him to think she's using him to be taken care of in that way.

Maybe paying for household repairs and getting the car washed is her way of taking care of him by providing rest from work.

I don't know your cousin, I'm just saying that based off what you've presented, concluding that she's stubborn and independent and that's why she doesn't let him help in this manner is a bit of a jump.

Being stubborn and independent are not bad things for women or for men. Stubbornness gets a bad rap.