Tricky social situation

I call on you my readers (if I have any) to help me with suggestions on how to deal with a tricky social situation that has occurred.

WE asked Miss K who she would like to come to her birthday later this month, first it was her whole class.. we convinced her that wasnt happening, next we said 4 friends... so she named them a b c d... miss A is not a possiblity due to her mum and I not being on speaking terms at all... we were once friends but that has long since disappeared, the two girls are at school together, girls brigade and church. Its not an easy situation to handle but I havent had to face this yet.

So do we blanket say no miss A cant come, or explain why she cant come, or do we invite her?

Help invited please