Party Clash Dilemma

[WineOhWhy]

I have booked a party for DD (still 6 weeks away) and was planning to hand out invitations this week. Unfortunately another girl in the class has just sent out invitaitons for the same date. There is a gap of 2.5 hours between one party finishing and the other one starting, venues are about 20 minutes apart, and I would say the children could live up to 30 mins from one or other of the venues.
I have paid for the venue in advance. I have tried to move the party to another date, but unfortunately the venue is not available on a Sunday for the next 10 weeks (and then we will be away), and the party cannot be on a Saturday for various reasons.

So what would you do? Would you go ahead and have the party, even though it will be a bit awkward for people logistally (and we might have 20 tired 9 yo girls). Would you speak to the other parents to see if they minded before going ahead?
Not sure if I will lose the money we have paid if we change to a different venue, hopefully not if they can rebook it to someone else which I would be hopeful of given popularity.

Unfortunately DD cant decide what other type of party to have, but she also knows some girls might not come if she has the party on the same day as the other one, so she is in a quandary.

I would have thought that at 9 they should be able to cope, the only thought that I have is whether there is anywhere to occupy them inbetween. Do you think the party list is similar (i.e. Have you invited all the girls). Just wondering whether for parents having the option to leave them all day (well 6.5 hrs) might appeal more so they can go and do something with younger siblings, rather than tooing and froing. Maybe talk to other girl's mother. 6 weeks is quite early to send out invites, explain that you had already booked etc. I would warn parents of your dd's best friends so they know that there are two parties that day if they want to make a choice.