Hi there Yummysushi. Congratulations on your new baby, you sound like you are a very sensible woman and it's to your credit that you are seeking advice from grannies. My advice in your situation would be to be present when your MIL is around your baby, if for no other reason than you will see and hear exactly what is being said and done. I have a friend, and also know another younger mum who is a neighbour, who both have major issues with their respective MILs and are pretty much no contact. I've lost count of the conversations I've had with them about it and to be honest it gets tedious. The neighbour gets so wound up for the week before her DH takes their child to the GPs house, and then spends a week forensically interrogating DH about what 'she' said and did. It has put a real strain on their marriage. My friend is similar, says she's fine with DH taking the children to grannies, but in reality DH has to go through seven stages of hell to make it all work. Just be there as a family unit and make it work for your husband and your child's sake as well as your own.
I've never really liked my MIL, for many reasons (insulting, passive aggressive, controlling of her only child), but we both make the effort to rub along for the sake of the family. When they visit, and the doorbell goes, I quietly say to myself "showtime!", I put a smile on and welcome them with open arms. I've encouraged my friends to adopt this approach (surely anyone can fake it for a couple of hours or so) but they stubbornly refuse. It really is cutting off their nose to spite their face as the tension this causes in their families is very damaging. Your in-laws love and want the best for your DH and your new baby, and that can only be a good thing. My children, who are adults now, have a lovely relationship with both sets of GPs. After 32 years, MIL and I understand each other pretty well. We're never going to be bosom buddies, but we've mellowed into our relationship and I hope she respects me as I respect (if not exactly like) her. She did say to me last year at DD's wedding, "you've brought them up beautifully", and I nearly fell off my chair - it's the first nice thing she has said to me in 32 years.
Good luck, and I think a PP idea of being pro-active and inviting your MIL before she starts asking is a really good idea.