Here's another way to look at this. My sister dated a guy in highschool, and our family loved him. We treated him like a brother. He was around all the time. Then they broke up. She went off to college and then moved far away. We still live here where he does. I still love him. It's been 30 years, and frankly, I still feel just alittle bit like he's related to us.
Then there's my ex-husband. He had a son from his first marriage. His ex-wife took the kid and moved across the country and wouldn't let him see or talk to his son. When we got married, I worked hard at getting her to talk to him and trying to get a relationship established with my step-son. We got her to send pictures for the first time in three years. My husband and I divorced after three years, and at that point we'd never got to see his son. I still have some of those pictures, and I still wonder about that kid and worry about him.
I was engaged to a guy when I was 20. His family loved me. My family loved him. For whatever reason, things didn't work out and I broke up with him. He never married (it's been 27 years,) but he moved away. I used to joke to his family that I broke his heart and he couldn't get married, and they agreed with me. But they still love me. When I see his sisters and his nieces and nephews, they show me pictures of the family, tell me how everyone is getting along, etc. I still love them, too.
Some people (like me, I hope) love quickly and freely, and once they open their hearts to someone, they rarely turn that person out. I've always thought there was enough room in my heart for all the people I've ever loved, and plenty more for whoever else comes along. I get along great with my ex-husband, even though his other two ex-wives don't speak to him. I get along with my present husband's siblings even when HE isn't speaking to them. I know I mention my sister's ex-boyfriend in front of her husband occasionally without thinking, because my kids are the same age as his and as the kids of some of their friends, so I see those people all the time. I love my brother in law, I don't want to make him uncomfortable, but I also refuse to quit loving the boyfriend. My brother in law is very secure in his wife's love and if it bothers him he never mentions it.
Your husband's mother may have let the ex-wife's children into her heart, and she may worry alot about their well-being with so many fathers in and out of their lives. She may think or know that your husband loves the children even though they aren't his and he doesn't see them. I would be very upset with my son if he were to marry a woman with a child, form a relationship with the child, and then just quit caring about the child when he divorced the wife. Maybe she wants to see a caring reaction from him to know that he isn't cold and heartless.
See, you're making the whole thing about you and respect for your relationship, but it may not be about you at all. The previous advise here to be extra nice to her and work to form a solid relationship with her is very good. Make her your helper and friend, and get her involved in her granddaughter's life and then you won't need to worry if she still talks to the ex.
And if she can wreck your relationship by talking behind your back and lying about you, then you don't have the relationship you think you have anyway.