B.H.
Both my children know that if one is invited to a party the other one will not be going. I would never call and ask for my other child to come. If I had no other option I would ask if it was okay to bring my other child but also ask how much it would cost to pay for that extra child. My daughter is 8 and my son is 5, I have done a party for them every year and I have never had a parent call me and ask this question. If you are okay with this mother bringing her son also but do not want to have the extra cost (since the party is going to cost enough already) just explain to the mother that she is welcome to bring him but the cost for extra children is such if all of the invited guest show!