You're in a make-do, temporary situation and have come up with a solution that lets your girls train and compete. That sounds pretty good really.
Definitely come up with some rules about what happens when new girls are ready to compete, then have a newsletter and let everyone know what will be happening in the future.
Let this one go. It really does sound like the coach has good intentions and probably thought she was just simplifying it for everyone. If you try and discuss it, you're just going to sound like you're nit picking and then the coach, who you said has done things unpaid in the past, will then feel unappreciated and it's a slippery slope from there.
@Becauseisaid 's calculation didn't account for travel and accommodation fees, so the coach's fees per session would have been less than in that calculation. Adding a session would have reduced the costs by more than that, depending on how much travel etc was.
Are the parents traveling with the girls as well? If so, if the coach has a daughter on team then she would have been traveling anyway, so it would be then reasonable to exclude those fees and then the calculation by
@Becauseisaid would be exactly right anyway
Coach by the sound of it is acting as Head Coach. HC gets to decide who goes on team etc. the sisters who are now included are probably thrilled to have this opportunity. Be happy for them AND get them to join the booster club.
If there isn't a gym owner, it always seems to be the case that HC and management have communication difficulties, I think you're in good company.
Ask her if she could next time refer the parents to you to discuss fees and you can then talk to her before making a decision. That makes it clear that you don't want to be bypassed, without you just sounding angry at her.
If something comes up that annoys you, ask her about it so it doesn't turn into a big deal when it may just be a misunderstanding.
Just keep reminding yourself (as you've said already) that there probably wouldn't be a team at all if this coach wasn't doing this. Sounds like apart from this she's doing an ok job as you haven't mentioned anything else. Support her, because she's supporting your girls and they get to compete as a result