I have kids coming up this age and employment seems to be a quagmire for them, so not looking forward to them coming back! In my day, you could get a graduate job with a good degree, and have enough money in a year or two to buy a little house!
She needs to be contributing for her own self esteem, if nothing else. She should definitely be doing her own laundry and household work and doing something else for the household, such as cooking a decent meal for the family, or cleaning the bathroom once a week, or value added babysitting. Knowing you can look after yourself and be responsible is good for self confidence and personal development (which is good for getting better jobs and leaving home!)
I did that for a short while, but was using my unemployment benefit for driving lessons and visiting my boyfriend (which got me out from under their feet) (and paid to have the cat castrated
). If she has expenses that are helping her further her future, I would allow that, but if not her father could take a small sum in rent and put it by.
I am all for this rent and putting it by business. It would be useful for her if she opted for further studies, and also if she left home, as it would reduce the chance of return!
If her father can see that it would benefit her and her future, rather than just be a way to prevent irritation amongst others, he may have the enthusiasm to carry it through on his own, which would be good.