I don't know your family dynamic or how certain requests might upset the balance with everyone so close, but I can tell you my experience with my own mom.
We were in Japan when Meg was born, and she was the first grandchild and long-awaited. My parents were itching to see her and wanted to be there for her birth. They are wonderfully supportive parents with whom I get along very, very well, but I really didn't want them there until we'd gotten settled and established with breastfeeding. I finally decided that this was good practice for me in choosing priorities and in taking a stand as a mother for the benefit of my child. So I asked them not to come until 2 weeks later. My mom was hurt, and still mentions it once in a while (they never did really understand why), but I am so glad I did it. I tried to explain my reasoning without making it personal at all, but was gently firm.
Birth is a private time for many women, and once things get rolling, you'll want to feel safe and secure to whatever extent possible. Arrange for that now, and you'll be happy you did. If your MIL can be helpful and supportive (maybe take care of your eldest?), that might be nice. But if you think she might not be, don't hesitate to help her make arrangements to stay elsewhere or to come later.
"It's much more fun once they can smile at you, anyway!" always works well, too.
Good luck, and let us know what you decide.
Kam, mamamama! to Meg and one more