Invitations and replies
Every party has one invitation link. The parent shares it however they like, and each guest's family replies there, with no account: who's coming, their age, and the waiver signed before they arrive.
The invitation
The guest's guardian opens the link and sees the party: whose it is, when and where. They choose Coming or Can't come, give the child's name and age, their own name and email, and sign the waiver if the package asks for one. They can ask for news and offers, and Send reply.

They're thanked and told they'll be reminded the day before. Change your reply brings their answer back to change, and a party that's full says so, so no more come than the package takes.

Who's coming
The parent sees who's coming from their party's page, with the invitation link to copy again, and changes the count until it locks.

At the door
On the day, open the party and tap Guests. Tap a child as they arrive, and again to undo a mistaken tap. A child whose waiver isn't signed shows Waiver needed: tap them, and their guardian signs on your phone, then they're in.

Add a walk-up for a child who wasn't on the list: their name, age and guardian, who signs too. Within the children booked there's nothing more to pay.

After the party, the guardians who asked for news and offers join your leads, with their yes recorded.