I'm sorry, OP!

I would definitely feel hurt, but maybe there was some strange calculus that she did that resulted, for some neutral reason, in your daughter not being included in the birthday list. FWIW, sometimes when a person is caught up in party planning, the pressure of everything can cause you to make some illogical decisions. So maybe she freaked out when the numbers of invitees were increasing and just drew a line that, objectively, was illogical and insensitive. The fact that she was unapologetic suggests to me that she thought she had a good reason for not including your daughter, and that it's not necessarily anything about you or your child.
It's pretty bad form that she held the party at the playground, where your child could see, but I'd just give her a free pass this time. If you like chatting with her and especially the other parents at the playground, and your daughter sometimes enjoys playing with/near the other kids (and is likely to do so even more as she gets older), then try to let it go. Take the long view, and look for what you can get out of the relationships, even if it's not ideal. I agree with 22:25 about going ahead and inviting everyone.