Relax and enjoy the ride
Can't add much more except one thing.. Pitching will tear your heart out as a parent. You will experience the highest of highs and the lowest of lows. It's an emotional rollercoaster like none other in any sport. It puts a huge amount of stress on the family and can help to make everyone stronger or break open some pain points. It will also require a ton of work on you and your family. It takes a village to develop a pitcher. That said there is nothing quite like seeing a shy kid develop into a warrior in front of your very eyes. As a dad I've learned that being a teenage girl can be very tough, but having to put in the time, effort and work it takes to become a successful pitcher helps develop the skills it takes to overcome many of the struggles that life can throw at a young woman. It's a crazy ride, but for us we wouldn't have it any other way. Good Luck and post here often!
A change up should be kept low so that if the hitter does time it, they have to make the secondary adjustment of going down to hit the ball also. 2 movements in the hitter doubles their chance of a bad swing. The combo of being able to read the pitcher's change up early and doing a backflip to keep it up in the zone is a deadly combo. - Bill Hillhouse
Do not think for a minute that your DD is starting too late. At her age she if she is properly motivated she will progress quickly. I would much rather work with someone like your DD who is a clean canvas than a kid with years of ingrained bad habits and misconceptions. It is a lot more work to tear the house down and rebuild than to build it right the first time.
I'm very happy/fortunate that my DD started pitching with a professional coach. The 4 pitchers on our 10U travel team all take group lessons and the two who had pitched before had to overcome a lot of bad habits, whereas my DD simply had to do what he instructed.
I'm not really able to add much that hasn't already been said. But those who have advised that pitching isn't a "part time" thing are absolutely right. It has to be a lifestyle, not something you dabble in if you want results. In this game, the more you touch the ball, the harder you need to work!!! So, pitchers and catchers need to work twice as hard as others in reality. Personally, when I was a young pitcher (12-18 years old) I pitched EVERY DAY trying to get better. I lived, dreamed, slept, breathed, ate, and poured my heart into pitching. I didn't do my best at school because I was too obsessed with fastpitch, pitching, etc. Obviously looking back I wish I had done better, but I may not have done what I've done, gone where I've gone and become who I am if I did things differently. So she has to want this.
This is pretty much what the coach who is working with her said. I am happy to say, she had pitching practice last Saturday and has been pitching about 35 pitches a night at home. I am hopeful that with a lot of mound time this spring and fall we will see how she comes along.