Honestly, I wouldn't do both. If I were invited to two parties for the same children within a couple months, I'd side-eye.
If the shower was before the birth, I'd feel differently but two parties close together with the babies in attendance can seem gift-grabby.
Rather than do both of them, ask your mom to help you with the Meet the Babies party. People (myself included) feel obligated to bring gifts to parties for children.
I agree not to mention gifts on the invite at all.