To answer your original question, I think you are fine with the amount of tennis, as long as she likes it. And mixing in soccer is great. Now on to my real issue, please don't take this wrong, but I am just in shock about what you say this child can do.
What you are describing would be a talent above anything even Rick Macci has ever seen. In my 20 years of being around all sorts of future elite kids, I have never seen a 6.5 year old who can do the things you describe. A 6.5 year old who can have practice "matches" with older kids, use regulation balls, cover the entire court....all while using proper stroke technique? Not only that, she is now able to work on strategy and topspin while chasing down regulation balls?
I have seen kids that age being properly fed balls that can do great things, as long as the coach keeps reminding them of their technique. Sonya Kenin appeared in USPTA videos and is considered as good a 6 year old as there had ever been, and she needed Macci to feed her the balls and could not play real tennis with regulation balls in a practice match setting until about 8. I have never heard of a kid who can play what you are describing, which sounds like actual solid tennis, with proper technique, using regulation balls on a full court.
And the kick in the gut for me....this amazing sounding, greatest prodigy I have ever heard of....is doing is with a 23 inch racquet! Once again an all time first for me, Macci, and any coach I can think of....a kid who can play real tennis with regulation balls, using a 23 inch racquet.
Hitting regulation balls coming off of someone else's racquet and covering a full court....returning them with "topspin" and hitting "inside out forehands".....with a 23 inch racquet? That hurts my arm just thinking about it.
The matches with "older kids" smells really fishy. Even if older meant 7-9 years old. Our kids by that age are using 27 inch frames and hitting 70 mph forehands. And even in NE, I bet the kids that age can wallop the ball pretty good. A 6.5 year old with a 23 inch frame would not be able to get one ball back over, let alone "hit inside out forehands". Heck, even our pros would have trouble against our 7-9 year olds if they had to use a 23 inch stick!
If the older kids are hitting the balls back to her nice and soft on purpose, that I can see. Sure, a kid that age could no doubt bat regulation balls back and forth with a 9 year old who is hitting them nice and soft on purpose. But actually playing to win the points? Why wouldn't they just blast the balls right at her since they have huge advantages in their size and the size of their racquets?
The icing on the cake....ball machine? Your 6.5 year old hits against a ball machine, shooting the often hard and dead regulation balls in those machines, with a 23 inch racquet? Any tennis coach that allows that should be fired yesterday.
Sorry dad, my hunch is that you and the pro are rushing kids along and they are having short moon ball rallies with regulation balls, and since the score is kept, thats considered a 'match'. My hunch is also that the technique used would make us cringe....bunted strokes, etc. If that is the case, slow down, get the strokes right.
The tip off is the 23 inch racquet and a ball machine. No adult would allow that to happen who has a clue about tennis. That leads me to believe the rest is awful, technique, etc. The same adult who would allow a 6 year old to hit with a ball machine and regulation balls with a 23 inch racquet would also have no clue what proper technique looks like.
I hope I am wrong, because if I am, you have potentially the greatest player in tennis history.