It's fine for grandparents and the grandchild to bond. Some children don't have such loving Grandparents or, in my case, my children only have Grandma because the other Grandparents passed away already.
That being said... well, Remember, YOU are the Mommy...but, by your choice, you let Grandma "take over." Your intentions were so that they can enjoy each other since Grandma lives away. That's nice.
Letting Grandma "take over" when she is around....and letting yourself just sit on the sidelines... is kind of counterproductive. You are then truly "letting" Grandma "take over." You can certainly let Grandma and your child have fun and do things...but how come you don't make yourself a part of that too? You don't have to be "invisible" when the 2 of them are together. As a Mom, with a strong personality Grandma/MIL... certainly I think it would be best to make your presence and your "leadership" of your own family paramount.
You don't have to be heavy handed...but maintain your role of Mommy of your daughter, you don't have to "delegate" that role to your MIL.
For your MIL to display jealousy and "compete" with you for the attention and love of your daughter is... well, I would be irritated too. MIL IS competing with you. This is not cool. And her "happiness" is based on "conditional acceptance" and how many events you make it to in a year? Good grief. How about YOUR own family and visiting them? Or does she compete with them too? That's another Oprah.
Anyway, back to the subject: When my MIL says something to my Husband, (she lives in another country) about our raising our kids...my Hubby always says "I'll check with Susan about that..." or he will tell her "We're fine, we have our own way..." In essence...you are "gently" showing her who is boss... and showing her boundaries. There is a pecking order... and a child's Parents are FIRST of course, over the raising of YOUR child.
Your child is enjoying her Grandma's unfettered attentions and probably less "rules." It's great she loves Grandma so much and feels close to her. Yet, don't make your girl feel "wrong" for that... she is just a child. Yet, at the same time, I would hope your MIL is NOT the type to try and tell your child things behind your back in order to gain her "loyalty." That would be real dysfunctional and plain wrong and childish for an adult to do.
Ideally, of course, you would want a MIL that respects that YOU are the Mom, and knows her boundaries. Well, she is encroaching on that already. Why can't you just talk with your MIL, adult to adult, in a reasonable fashion and express to her your concern? Maybe, to give MIL the benefit of the doubt... maybe she does not realize she is UNDERMINING your role?
And, where is your Husband in all of this? He should be supporting you, you are his wife and this is his family. He's a grown man and not a boy. He could also speak to your MIL if this is a real problem. If she leaves the room and pouts and acts unbecoming like this... then so be it. It's just not right to pit a Parent against their own child. (ie: you against your own child). Because this is what your MIL is doing.
Again, your daughter is 4 years old and you want her to grow up with good feelings about her Grandma. Children need their Grandparents too. There was a time, when my own Mother would get "jealous" when my children would pay more attention to other people and not her and she would comment in front of the other people! I would "remind" my mother, that THEY are the children, SHE is the adult so let it go. Sure she didn't like it....but she knew I was right. And now, she has come to terms that she won't always be the one getting attention. I would not let her make her "jealousy" a "problem" in MY family. No. Boundaries.
Also...as my daughter has gotten older, and per her maturity... my Hubby & I ALWAYS remind our daughter that no matter what... WE are the ones who decide things for her in important matters, and that WE are her "Parents".. not Grandma or Aunty. You see, there was a time when my girl would get "confused" about who to listen too...and who to follow....as Grandma & Aunty are strong women (with good souls), and they would tell my girl things that were outside of their "jurisdiction" so to speak. Because of that... we had to "step in" so to speak, and quite diplomatically tell them that THEY must ask my Hubby & I for any decision or discipline matters concerning our child and it is WE who will decide. NOT them.
THIS has clarified much, and put things in perspective for them. Also, our daughter is much happier and less confused about "who" to listen to. WE are her parents, and she comes to us and is more peaceful about it. If Grandma or Aunty tell her something, my daughter will always say to them "Wait, I need to go ask Daddy/Mommy first..." Meanwhile, Grandma & Aunty are less "possessive" about things. And we all still get along, no problem.
Hope this helps. Just my opinion. I'm sure there will be LOTS of other suggestions and experiences.
Hang in there, and take care. Everyone has pangs of this sort of feelings, at least you can admit it and seek other perspectives on it.
Take care,
~Susan
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