It's a personal choice, but for me, absolutely not. I love my parents and love spending time with them, but for the brief periods I've lived with them (since leaving for college a decade ago), I've found that there is a large benefit to living separately. I'm out there on my own, and live a more independent life. Since you have a family, I think this would magnify this (spouses can usually only take so much of the in-laws... not because the in-laws are bad, just because the effect is multiplied when it's not your direct parents). I guess a potential benefit is that you have parents right there whenever needed to take care of the child.
If you could have completely separate living quarters that are separated by walls and doors, then it might be different (e.g. you in a basement / separate floor, where opening that door is generally off limits).
For me, though, there are other ways to save money that don't involve sacrificing the independence... all extensively documented throughout this site.
Again, it's a personal thing, and if it works for you, that's great. But for me, and I'd think many others, absolutely not. I understand it makes sense financially, but this is an area i'd skimp for only in dire circumstances.