Reddit mentions of Midnight At the Dragon Cafe

Midnight at the Dragon Cafe by Judy Fong Bates - I'm not sure if this is exactly what you're looking for but it's similar. It's a Canadian book so it might be difficult to get your hands on if you are outside Canada.

A Chinese immigrant family comes to Ontario, Canada to start a new life and they open a Chinese restaurant in a small town in the middle of nowhere. The mother struggles to adapt and doesn't want to learn English, she longs for her wealthy family back in China and is really unhappy in Canada. The family works their asses off to make the restaurant work. However, when the older son arrives, secrets from the mother's past begin to come out and everything begins to unravel.

It doesn't really span 3-4 generations but at parts it involves the mother's parents and grandparents a bit I do believe and down to her young daughter's life. There is a ripple effect between the generations from what happened before they moved to Canada.

This one kind of surprised me. The Toronto Public Library has a program every April where they select one book by a local author and designate it as their Keep Toronto Reading One Book community reads book and host events and things around the book. Last year they chose this book so I thought I would give it a read. For a good chunk of the book I was feeling like it was just OK but by the time I was finished I loved it. The events just sort of compound on top of each other and by the time you're done, you realize what a dramatic journey you've gone on. I quite enjoyed it.