I completely understand your situation. I'm not even talking to my sister right now as she pretty much told me I'm a horrible mom and that all my complications are my fault (I'm not making this up...). Her and my mom also steal my "spotlight". Like when we finally set our wedding date, my mom who'd been engaged for years picked a date finally, 2 months before our wedding. And then my sister who literally had just gotten engaged picked a date 3 months after our wedding... Oh and they'd both been married before... Isn't family just amazing?
Anyways, I'm in the same camp as you. I'm thankful that our hospital calls us first before letting visitors back. I think me and DH have decided we're just not telling anyone, not even parents, until 24 hours after baby is here. That way we can bond, not worry about phone calls and visitors, and just enjoy baby's first day alone together as a new family. And my husband, after my sister went off on me with all this crap, specifically said she's not allowed to visit until he says so. And my husband typically stays out of my family drama.
So, do what you think is best for YOU and LO. This is your baby, your birth, your labor. As to how to tell sister no visiting for X amount of time, I have no advice b/c I haven't covered that with my mom yet...