If it were me i would had spoken to my friends before the invites went out (as a group if I could) and said I have invited all of you guys to the party just on your own....hope that's Ok but no offense if you cant make it....then sent the invite with just their names on it. That way you have made your wishes clear. I would not be insulted if I had for-warning it was only me and if I didn't want to go without my partner/kids then I would feel OK saying no and still keeping the friendship.

I personally take my DD everywhere (DH is a shift worker and not home most weekends) so I would have the choice of declining or bringing her. I would 'ASSUME' she was invited to a kids birthday although recently i got a baby shower invite with only my name on it and after checking DH was working I did speak with the expectant mother and she said it was fine for DD to come. So I guess for me the type of event would dictate more who I would assume was invited.

I do understand your frustration about the invite but I do think there were assumptions made on both sides....you assumed that all of these people would realise that the invite meant only them when it seems the (majority of people even on here) would assume differently.

I hope you have a great birthday party for your daughter and hope it all works out perfectly.