Your spouse needs to tell his/her parents to back off. It’s your child. You decide. End of story. Me, I carried and nursed my babies until they were old enough to unbutton my blouse and name my boobs. By then they were walking so it was time to quit. Given plenty of food they didn’t seem to mind.
Nursing is another issue we have. DD is allergic to formula (the Dr made us try it because she wasn’t gaining as much weight as they wanted) she lost weight on the formula. So of course I am nursing, but MIL keeps pushing solid food and juice and I am surprised at how many others are surprised I am still nursing. I plan on nursing until she self weans (or like you said starts naming my boobs).
DH does tell his parents to back off but that doesn’t stop them from their refrain. I had health/feeding issues and so I was held all the time by either my mother or my grandmother. My mom couldn’t handle me crying so they didn’t do cry it out either.