I wouldn't go on a Sunday morning, to a lot of people that is when they get to sleep in, have a family breakfast, do little things they like to do in their jammies, and if they care about religion they might go to church.
So I would decline a Sunday morning invitation. Just because it's on a Sunday.
Now if it was on a Saturday I'd get the kids up and feed them before we went. Your menu does not sound like kids would eat it at all. So I'd have to feed them before we went.
That leaves you having a ton of food left over because it's not the kind of food people eat.
Are they coming for a birthday party of family get together? Because if it was me I wouldn't feed them at all, people come to a birthday party to eat cake, open presents, and play. They don't come to a birthday party to sit around and eat breakfast.
Family parties are a bit different than a regular birthday party though. If it were me, just having had a C-section I'd make it pot luck and extend the time because every single person is going to want to hold the baby, bring their new baby gifts and see you open them, maybe even try little outfits on the baby, etc...they're going to want to pay all their attention to the new baby.
Have a formal party for the little one, don't serve food, only cake and a drink. Focus all the attention on her. The baby will get lots of attention anyway but without the sitting around eating breakfast and allowing the kiddo's to run amok they'll all be ready to leave at noon.