I hesitate to offer any advice here, but from experience would suggest that you and your husband nip this in the bud before the situation gets out of hand and feelings really get hurt. As a new Mum (or are you a Mom?), it's obvious you want to do the very best by your little one. I can remember with my first child frantically sterilizing nipples every time every time they so much as touched a counter top or anything (baby bottle nipples
. )By next baby, so much more relaxed and not quite as stressed to do everything by the book (and 'the book' changes all the time - it always seems the most current advice is the best, until the next lot comes along). However, it is for you as parent to your child do what you see what is best in your child's interests in your own situation. Just as your MIL did when she had each of her own children, and her mother did, etc. (May be ask her how HER mother's and MILs parenting differed from hers). Though she may well have some gems of advice from her own experience as a mother or nurse which may prove helpful, so please don't brush aside her remarks out of hand.
Reading your later comments it does sound like your MIL is having a hard time transitioning and navigating to the newer role of Grandmother and a more supportive role rather than the leading role. Your MIL's tears seem like a means of control, she may have used this emotional blackmail in the past to get her way and is totally un-acceptable imho. By saying 'poor baby' when asked to stop feeding as there had been an error measuring the formula shouldn't have elicited that response, unless she was trying to use some sort of guilt. But then again, it may just have been an offhand remark, not aimed at anyone, just granny enjoying feeding and bonding with her grand baby and her having to stop.
If these miscommunications continue it could well lead to
bigger issues, does your husband want that?. If not, he should really be the one to point out you are all in new roles and how important it is to work together to be supportive of each other. MIL probably thinks she is being supportive, but perhaps she is coming across as Mother and making you and your husband still feel like children. Hard to make that transition sometimes.