I think you need to be more assertive, veexox
As I understand it, when you talk to your MIL you are saying two things.
Namely
1. I'm so pleased my dd has a loving grandmother.
2. Could you butt out a bit day to day.
The problem is that all of us tend to only hear what we want to.
Your MIL hears the first and ignores, downgrades, minimises, the second.
We all do this - conversations are complex and nuanced, but we like to take away a simple message, and if possible a message that pleases us !
I feel that unless you start being more direct and blunt in both your words and actions, she will never change.
I don't think this is being unkind. If she doesn't change then further down the line, it's possible you will just crack and go no contact with her.
And then, she will be aghast and hurt and will genuinely say
what did I do wrong
All because she didn't hear the second part of your message. . .