well her kids don't even know my kids for one, there will be other kids there but they are from our play group so they are all friends, and for two the party isn't for her kids it is for my child.

If she had of turned around and asked could they come.... maybe a different story, but she didn't she just said they are coming. I know if i was just invited to a party than i would clarify if my kids and husband could come i would never just invite them along without asking!
There are also a few little children around and her kids are a bit older, and with their lack of good behaviour the last thing i want is the other parents to be not enjoying themselves because they are worried about their younger children around these kids, and the last thing i want to be doing is policing kids in my house that really have no respect for other peoples belongings!
The other ladies don't have a problem with coming without their partners, although we would love for their partners to come we have even turned around and said feel free to invite them but they don't feel it is something they should go too and are looking forward to an afternoon partner free