This sort of happened to us in kindergarten. But it was during the school year and i just descretely sent a note to the teacher saying my ds insisted he was invited but that the invite never made it home, and I just asked her if she knew if there was one, as in did ALLL the boys get invited per school policy. The invite had infact gotten misplaced it was slide inside a book Ds had been reading. I called the mom and explained an got all the info and went and had a great time.
I think if your dd is celebrating her own bday that weekend, then don't even worry about this other party. at least now you know if the 2 that are sleepign over happen to mention it, you won't be caught off guard.
I think the best policy since you don't have anyone that can delicately inquire, is to just forget this other party is even happening, enjoy your own DD's bday and if for some reason your dd was to have been invited just say you wondered about it but when the invite didin't show you figured they needed to limit it for what ever reason. these things happen, i do hope little suszie had a great time, blah blah blah,
I'm wondering what was so confusing about the other invite, and i'm also wondering if the other biday girl didn't have your address for some reason.
edited
oh that makes sense the date was wrong--- my son has a friend whose mom is not from this country and she has sent some wacky bday invites, That's what i though maybe was going on in this situation ... a cultural issue, but apparently not.
I stick by my original answer, if you call and she was invited well ok, if you call and she wasn't the SUPER akward. by leaving it alone, the akwarness is minimized.
forget it and have fun at your own party.