You really need to just sit down with the coach who makes the team decisions and get a straight answer as to why your dd is not eligible for their team.
If the coach said "she's not ready" for team, that indicates to me that the coaches feel there is some maturity, work ethic, or other issue going on, especially since you are noting that she does have the skills for team. If they feel she is too old, they would have told you that. Gyms that have an age "policy" for team usually are quite honest about it. They will not string you along.
You mentioned she got bored in intermediate. They may have seen some behaviors then that led them to believe she was not mature enough - even if you did not visibly notice any behaviors. And given that the 7/8 coach was impressed and then presumably talked with the other coaches and you have heard nothing since leads me to believe it is not the skills, but something else. Obviously, this is all speculation, not knowing your dd, which is why I would be speaking with the hc (or whoever makes the team decision) to figure out exactly what is holding her back.
As for the coach doing the private lessons and then not paying attention to her at other times, that is pretty common. They are very busy. It is nothing personal. The coach paying more attention to the tv than dd would irritate me and I wouldn't have paid for any more privates after that incident, but it doesn't mean that the coach is against your dd, just that she is not very professional. As for the privates themselves, it is not normal (or desirable) for rec kids having to take privates on a regular basis in order to progress. If that is the policy of the gym, then they are just trying to squeeze money from their families, which is not the typical practice of most good gyms.
One more thought - and please do not take this as an accusation, as I have no idea if this pertains to you but something you need to consider. Some head coaches make decisions about who to put on team based on parent attitudes. If they feel the parent is going to be a major pain to deal with, they will avoid putting the gymnast on team. From your note, it is clear that you are becoming more and more frustrated/irritated. If this is showing in your interactions with the coaches at all, it may be working against your dd.