I'd just keep the party as planned and not send DD to the other party. My DD wouldn't last 2 parties in one day! If it wasn't going to be a big deal for you, i'd change it by half an hour, but if thats a problem then i wouldn't worry.

As for worrying about if people will go to the other party or not, it's probably just giving you gray hairs for nothing. It's not your fault, it's no ones' 'fault' really, just an unfortunate co-incidence. People will do as they please regardless of your worrying.

Your DD will probably still be excited about her party and all the pressies she's going to get. I bet she will have soon forgotten about the other party.