ETA: Saw your SWH - that's great. That once happened at one of my daughter's parties - little girl had a dance recital practice, that she couldn't miss, but she made it to the tail end of our party (for cake and fun) and it was great. We had saved her a piece of pizza which she appreciated because she was starving from the dance. That worked out great then! I think to go with the flow, and just play it by ear is the best you can do sometimes. I find we moms sometimes overthink (I know I do) because we want our kids to not miss out. The thing is, they don't care half the time - it's us moms, trying to do the 'right' thing all the time. This seemed like a great compromise! Glad you found a way to make it happen. Fun :)
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Well .. doubting what you decided because of how other people were to you, let that go.
Are you worrying about how people might judge you? Not sure I'm following. Or is it that's not how they would have handled it?
Personally, we would have probably picked the birthday party - only because, I think your daughter is quite young right? For us, those classes changed yearly (new kids), and we would have viewed it as a chance for kids to bond and have fun. Sports at that age were just for fun. That is how we approached it.
The whole you don't miss a game or let teammates down - came into play a bit later when they were older. That's a valuable lesson, but we covered that at a later age. In grade primary/one it was still let kids be kids.
As for moms telling you a party is coming up - unless it's a close friend, I found that a bit hard. We had that happen once, another invite (from close friend came in), we still hadn't had actual invite from mom #1, and our child wanted to go to close friend's party. We'd only told her about party where we'd received actual invite. We didn't even know if party #1 was still a go.
I think you don't over think, you trust your gut, and just go with it. No one will have the same answer. It's kind of a parenting style, whatever works for your family that week kind of scenario. I think whatever you decide is absolutely fine.