I wouldn't want OP to feel that she is being picky or unusual, because she is in a odd situation to be sure. Friend 1 is only being a bit tactless and no worse crime, but there is nothing wrong on a public forum to canvas opinion about a perfectly understandable reaction.
To change plans after they have been set is strange: why not get the threesome out the way first, and then think of how to get a big group meet-up going - maybe as a regular thing. (Open air would be best during these times, obviously).
Putting other two mums on the spot by asking, which two out of the whole cohort of class mums would be most welcome is really tough for them. What do you say? Why should you be forced to make a choice of who seems more companionable/fun/ things in common than another mum, when presumably you don't know any of them well, and it isn't even your idea to get together in the evening!
If it was Friend 1's house and she was cooking, then fine, she is hosting and she designs the evening, taking account of all kinds of considerations, but suggesting that you could go out in the evening again as you did once before is not really 'inviting' in the same way. But she isn't really giving other two mums an option to veto her initiatives in a way which doesn't look sullen and precious.
It's fair, I'd say, that if you make good friends at the school gate then you are entitled to meet up in twos for the purpose of chatting about things closest to your heart, without it being the case that you are behaving in a way that leads to others feeling excluded. A three is a bit like a two - special friends who feel safe speaking frankly.
The proof of the pudding will come after. Only a few months down the line will OP be able to see if Friend 1 and herself have the makings of a decades long friendship and whether, additionally, a lovely inclusive dynamic is being established for that class of mums.