Hi there. Sorry this is going this direction. I think sometimes older people do tend to try to tell us what to do and it can rub us the wrong way. Often, it is out of a good place though and that person can have some true wisdom to share. It sounds like, though, that your BD's grandma goes about it in a way that you feel belittled or like you are doing things wrong and is too pushy.
So, I would say to her "that's a good idea. I'll think about that." Then think about it . . . . and if you do think it is a good idea, follow through with it. If not, then you say to her "well, I thought about what you said and decided to do X this way instead. I really think this is best but thanks for trying to help me."
This really sets a tone for the fact that you do want her to be a part of your life but that you are going to make the decisions yourself.
So, take the good of elderly people in your life and leave the bad and just be polite.
I have a sister that I adore. I mean, she's great. And a great mom. But she is very forceful about 'knowing everything'. I just listen to her and show her respect while living my own life. So, that's what you have to do with extended family of your BD. Don't let it get to you. She's hitting on that tiny bit of insecurity you have inside and it makes you mad instead of thinking "whatever lady".
I don't know that I'd say a whole lot to your partner. Because family is family. Most men do not really want to be in between the women they love. So, just try to get to a place of being polite acknowledging her and letting her know that you will do as you are going to do.
good luck
Tell her that there are new laws on child care and new studies on what is best for children now days. A lot has changes since George Washington was president and she had her kids. Say you don't want to offend her but her way is no longer the best way and is not appropriate child raising or approved by doctors or cps. I know it sounds crazy but I had to do that with my own grandmother with my first. I even had children's services to visit with her and explain that things have changed and her ways were not appropriate. It works for everything which is what so good about it, from feeding bathing to play time and discipline. Good luck I feel your pain and aggravation.
Lol people are going to try and tell you to raise your child no matter if you know them or not. I had a little old lady tell me all of "advice" on rasing the perfect baby while stuck in line at Walmart last week. You just have to raise your child the way you feel is right.