You definitely don't sound bratty! You want to spend time with your baby!
I've been stressing about the same thing for months. My MIL has been saying for years that she will "take my baby until she's two" because that's what her family did (crock of sh*t, btw) and I know that when she comes to visit all she is going to want to do is hold the baby. I can see her trying to do everything for the baby and not letting me, and especially my DH, have the opportunity to care for our daughter ourselves.
I wanted to try to honor her being a grandma for the first time, but I have finally come to a place within myself that if she can't honor my requests as a FTM, she will just have to go along with my plans or leave.
Thankfully, my DH is on the same page as me, and I've been already talking about ways our visitors can help us while we are at home (grocery shopping, light cleaning, cooking, freezing meals). I've made it pretty clear that anyone who is to visit may visit with the baby, but it is our job to take care of her and anyone wanting to help can help take care of us not her.
Hopefully things will go more smoothly than I imagine them going in my head, but in the end, I guess it will be our first step in Mama-bear-hood and putting our feet down for what we feel is right for our children (and parents having those precious first weeks and days to bond with their new babies is absolutely what is right!).