I would tell her it's her loss if she can't act like an adult for a few hours. I hate when parents try to lay guilt trips on us.
She suggested it, she should bite her tongue for 3 hours and get over it. We had 2 joint parties for my oldest and never again. It works out better for us, our parents just don't get along. I mean, they do but the tension is so bad I can't deal with it.
I'm sure you will have a great time and Melanie will have a great birthday! She should be the only one there acting like a 1 year old anyways