We do once a week for a couple months going into season. Right now once about every 3 weeks during season. We will probably not see the instructor for most of the summer, then a few times before fall ball and travel team tryouts.
I think dd and you can have a pretty good idea of what they should be doing after just a few visits and can work on your own without taking a second mortgage on the house.
As an instructor, I recommend once a week over the off-season, then practice on your own at least a couple of times before the next lesson. Too much instruction can be as bad as too little. Especially at 10U, pitchers need time to experiment, learn, and incorporate the lesson into their pitching.
Once a week, as close to year around as possible. They are going to lose their skills quickly if they take 3 months off.
I equate it to piano lessons.
Unless, the team coach is a very good pitching instructor, any coaching someone else is giving the player is probably wrong.
I see it happen, though. One student was gone a year! She comes back and Mom proudly announces that she is pitching every game. Oh, my gosh. She had developed SO many bad habits. She looked more like a bowler. There wasn't much I could do at that point.
You don't want girls pitching without proper instruction. It can be too hard on their bodies, if they are "off" at all.
Once a week. Daughter has been going to lessons almost 2 years. Since last August, my daughter has missed 4 lessons. 2 for Thanksgiving and Christmas, and 2 for illness. Although, daughters pitching coach had given girls' lessons on Christmas day, and at one o'clock in the morning.
At 12U, coach is constantly "fixing" things. Not big issues, but little things. I'm sure at 10U, it's even more. Call it "fine tuning". I know for my daughter, if she learns a new pitch, it can affect her other pitches. A big one for us is the curve ball she is learning. It really messed up her peal drop. Don't know why, but it did. So, she had to change her drop to a roll over.
From what I understand, there are 2 ways to throw every pitch. And if you are good at one, then learn a new pitch, it can mess up your good one. So, pitching is a constant learning and adjusting thing. I don't think a pitcher ever stop learning, even through college.