Hi Kristi,
I'm a mom and a g'ma. We've had issues on both sides of the fence. My in-laws always played favorites even between our 6 kids it happened. You know sometimes we have to just shield our kids the best we can and love them and squeeze them pretty close when something like this creeps into their lives.
It's so hard to be the mother in law too. It really is; I'm sure some people have horrible experiences with their inlaws like I have but it's also hard to BE the in law...LOL
I like the idea of inviting all of the kids, g'ma and g'pa out to places. It would make her feel special in your life and that you are accepting her too. It's not easy being the one who caves in, but sometimes we have to do that just to keep the peace. If that doesn't work, give the duty of inviting to your hubby. My InLaws do not like me, that's ok, I only have to see them a few times a year! But I will never stand between them seeing their grandkids even though it is always on their terms. sigh!
Your kids will respect you in the end. They will also learn what NOT to do when they are adults and face similar problems. Just as you learned to "play" endlessly with your kids. You've broken the cycle, congratulations!