Hmmm...
What's most disturbing to me in this thread is the amount of people calling breastfeeding children of a certain age "perverted" or likening it to a sexual act.
Obviously, these people can't have ever breastfed or they'd know damn good and well there is NOTHING sexual about it. In fact, there was surely nothing to make me feel LESS sexual than when I was breastfeeding. What's gross to me is that people actually think they are one and the same just because they are both functions of the breast.
If you can't guess, I nursed my ds well beyond what our society considers normal. He was 3.5 years old when he finally weaned and it cracks me up when people suggest that I was just in it for me and that only *I* liked it. Uhhh...yeah no. I was SO over it. But it was best for my son and his immune system. No other liquid or food could offer him what MY milk could...because as we nurse our children, our bodies actually configure the milk to be best suited that THAT particular child. Cow's milk would never come close. A juice box? HA. What a joke.
I don't honestly think I could have gone much longer because, as I said, I was absolutely DONE. However, I remember as a new nursing mom just wanting people to respect my privacy and rights as his mother. I think a nursing mom has a responsibility to extend that respect to others around her. The SIL in the OP is obviously NOT respecting anyone but herself and her own children. She's also setting a bad example by steam rollering anyone who dares disagree with her. She clearly is setting herself apart socially and not wanting to be a part of things.
I agree, it's your house, your rules. Be open and honest. "We love you and the kids. We want you there at Thanksgiving but none of us is comfortable with you nursing the older kids in front of everyone. Is there any way you could do that in a private room?" If the answer is yes, great. If the answer is no or an argument shut her down RIGHT away. "I'm sorry we can't find a compromise on this one. Maybe you can join us next year." Don't engage. She seems to be one of those miltant people who get a kick out of challening people's beliefs and comfort zones. If she's like that, she'll love the rise she gets out of everyone so just don't engage her.
Sorry you're dealing with this OP.