So the child's mum technically has her four nights (Monday to Friday), and the child's dad has her three nights (Friday to Monday).
Mum works and the girl goes to nursery Mon-Fri (sometimes skipping a Monday or a Friday). Together with her mum, the nan (who also works) they manage the drop-offs and pick ups and having the girl at home for two of those four days, but (because of work commitments?) they use mum's dad, the granddad, for wrap-around care on the other two days. Perhaps it worked out more convenient for granddad to keep the child overnight rather than bringing her back home late when mum finally gets home from work. Either way, it is how mum organises her four nights around childcare and work.
Dad has his three nights on days when he works. So he organises his childcare and work commitments by using his parents for two nights, just as the mum uses her dad for two nights.
The mum can't really blame the dad for foisting the child on his parents for two of his contact days, when she foists the child on her dad for two of her contact days. Nor he, her. They're both the same.
What they need to be doing is re-arranging their working hours, and/or their contact days, so that mum has the child on those days when she isn't working (e.g. weekends, and she only works part-time so will have some other days off) and dad has the child on those days when he isn't working (e.g. Sun-Tue night).
Then they can always ask either set of grandparents for help and childcare, e.g. if mom wants to go out on a weekend.
But tbh OP your brother sounds like he is quite content with the situation, having his contact nights on days that he works is a convenient excuse for not having to step up to his responsibilities.
The mum equally seems to be happy to have her weekends free for going out, rather than having her daughter to look after. She works part-time plus lives with her mum who also helps, she should be capable of arranging working/contact days to be able to actually have her daughter on the four days that she has her.
OP it is in your and your parents' interest to get the dad to step up. If this continues, sooner or later the girl will be on SS radar, your brother might lose his contact days, and there is a good chance your parents (and you) will no longer see your DNiece. At all, ever. You have a lot to lose here.
Your parents are enabling your brother, but this won't last, and when it all falls apart, your parents will have zero rights. It will all depend on your brother. If he steps up as a parent, he and in turn your parents and you will remain involved in your nieces life. If he doesn't step up as a parent, the chances are that sooner or later he will have much reduced involvement with his daughter, which will mean that you and your parents have near zero involvement. He might lose his contact days, or only have her one afternoon/week or supervised contact (due to being an alcoholic) or whatever, either way it might mean you and your parents barely see your niece anymore.
In turn, the mum needs to step up as a parent as well. She has a lot to lose as well, as do her parents, who seem to be enabling her just as yours are enabling your brother. But that is not your concern.
The doll's house is neither here nor there. If you can't get your brother to step up, you might soon no longer be able to see your niece at all, and having a toy in a house she hardly ever visits would be fairly pointless ...