Have you thought about what sort of relationship you'd like your child to have with it's grandparents, and what sort of relationship you'd like to have with them after the birth?
That's not a trick question, I'm just genuinely curious.
You have a better understanding of the situation than anyone here does, and there are a lot of 'subtle' things that they might be doing that might not come across in the text. I know my wife and I just went to a 'Baby Basics' class where we paid someone to give us 'baby advice' for four hours.
I don't really have any advice for you, I certainly have some of the same feelings/fears about my parents/in-laws being too involved or not doing things the 'right' way. One thing that makes me feel better is to remember that my in-laws raised my wife and her siblings, and my parents raised myself and my siblings.
By any objective measure my parents/my in-laws are drastically more qualified to handle a baby than my wife or I are.