The short version is that the rules have been somewhat fuzzy on 36 vs 37 weeks, but in the upcoming rule revision one of the changes is to clarify that 37 weeks is the lower limit.
Info about rules revision:
It took me just over two years for AF to come back after DS1, and we got pregnant the first time we tried after that- I was 35. I had a Mirena after DS2, so it didn't come back until I had that removed, and we got pregnant after my first cycle, at age 39. Long absence of menses didn't indicate any reduced fertility in my case!
Ditto on the Fisher Price Healthy Care Deluxe Booster- much more useful for much longer than the Bumbo. I've used ours with all three of our kids from 4-5 months until 3 or so- when they were old enough to sit in an Ikea youth chair. We have a Bumbo, too, and it lives in front of the toilet in the master bathroom so I can poop without a baby on my lap.
The other approach I've found effective with criticism from grandma or other older people is to cite the baby's doctor- "The doctor is very happy with how fast he's growing! He says it's very important for him to nurse exclusively for at least six months before we even start solids, etc." They're usually pretty ok with deferring to the pediatrician. They don't really have to know that the doctor you're referring to is Dr. Sears and that the advice was given in a...
Have you asked her about it? If she's bringing up the topic of weaning, IME she's a lot closer to it than you think she is. You can talk with her about what she'd like the plan to be, and you don't have to set it in stone, just kicking the idea around is planting seeds. She really will wean in her own time, but you can certainly lead her to that conclusion.
I don't know if this helps, but I had a LEEP with conanization done in 1997 and went on to have three uncomplicated vaginal births in 2003, 2007 and 2011- all of them went over 40 weeks. I had talked it over with my gyno pre-pregnancy and he said my cervix looked good, and that it was highly unlikely to ever cause any issues. And it didn't!
I hope you have an uneventful pregnancy and birth!