I wouldn't worry about it being late sending out new invites. Send them anyway! Perhaps have a quick chat with the mums in the playground and say you really hope their kids can come, it's a bit last minute, quite disorganized - sorry - lessons learned but would love it if they could etc.... Invite the parents too. Just have fun. Don't fret so much. Maybe think about booking something that is a bit more flexible if people don't do what they said.....