Hi, K..
In your note, you don't mention if your daughter is asleep or resting when your MIL picks her up and dresses her or if she simply hears her and responds at the end of nap time. As long as she is not waking the baby, there is really no harm done. Relax and enjoy the moments when someone else can help out. Unless you have an outing planned, does the outfit really matter?
Please keep in mind that everyone is different, and your little girl will benefit from developing different relationships will all of the people who love her. When you share her, you give her an incredible gift--the chance to get to know other family members and friends who can each become a unique part of her life.
As far as taking her to a different room, consider this perspective: If everyone in a particular room is chatting, enjoying the TV or otherwise involved, maybe grandma is looking for a place where she can enjoy baby with fewer distractions. And if she doesn't play the same way that others do. . why does that matter?
As a new mom, you are probably tired, perhaps a bit insecure with all of the new responsibilities, and your body is just returning to normal. It's perfectly natural that you feel irritated when someone doesn't do things the way that you would. But, just because something is different doesn't mean that it is wrong or that anyone is trying to take over for you. Keep things in perspective.
I have three children, and I have encouraged their grandparents, aunts and uncles and close friends to spend time "alone" with them. Children need to know that mom and dad are not the only ones who love them, who will protect them, or with whom they can express their feelings. I know that it is impossible to imagine right now, but as your little girl grows (particularly during her teens) there may be times that you may not be the "right" person for her to confide in. Helping her develop strong relationships with people that you trust now ensures that she has connections under any circumstance in the future.
No one can or will ever take your place. You are the mommy. Be secure in that. Give your little girl the chance to explore other relationships--The world is an amazing place, and every encounter is an opportunity to learn and grow--if you look at it that way.
There may come a time when chatting with your MIL is appropriate, but do navigate such conversations with care. Be sure that the "issue" is worth the possible consequences. Talk with your husband and get his feedback as well. He might be able to offer insight into his mom. . .or talk with her himself so that she is more sensitive to your feelings.