The whole birthday party thing has caused me more angst than most any other social aspect of parenting. I have agonized over lists, worried about hurting people's feelings, struggled with limiting the numbers when there was limited space or when it was in a place that wasn't appropriate for younger siblings (like the year we did a party at the indoor baseball field and batting cages. What were we thinking????) : )
What I've finally come up with as the kids have gotten older? It's their party and their guest list, so they get to have more say in who they want. Sure, when they are in preschool, you control the list. As they grow, you have to let them make choices. "Susie, you can have 15 guests at your party. Let's make a list."
And maybe, that's what this mom did. Maybe her daughter just wanted her girl friends at the party. Not because she doesn't like your son or consider him a friend. Just because she's a kid, and at that age, kids start to have their own ideas and make their own friendships outside of what their parents have formed for them earlier in life. It's also pretty common for parties to start becoming more one-gender events as the kids get older.
In addition, I'm guessing from what you've written, your son is the 4 year-old. If I were hosting a party at an ice-skating rink for kids this age, for safety reasons, I'd want to limit the number of kids and ensure that each child had a parent with them to help. Your time would be split between a 4 y/o and a 6 y/o if you had both there, and 4 is pretty young to be left alone at any time on the ice. (I'm saying this as someone who has been ice skating since age 6 or 7. Just last December, I fell on the ice while skating with my son and nieces and suffered a very serious concussion that resulted in complications and a long healing time). What I'm saying is there is a safety factor to be considered here.
I would not ask to bring your son. It's just my opinion, but I feel that is inappropriate and actually rude to ask that of hosts of the party. If every invited child brought an uninvited sibling, parties could end up with 30-40 or more children (especially true when entire classes are invited). Most homes aren't set up to handle that many children safely, and in a venue, the additional costs to the hosts would be steep.
Regardless of the reasons, it is the other child's party and the other family's decision. You've to let this go because with kids as young as yours, you have a long way to go in the birthday party world. I get that it's hard with little ones, but children have to learn that they are not invited to every party. It's just one of those life lessons that we all have to learn. Don't skip the party because of this.
Regarding your son's party next week, haven't you already sent invitations?
If you haven't, you should go ahead and invite the kids you had already planned to invite.
Hope this helps.
J. F.