Re the tryout team - you need to ask some questions - both of the coach and your DD. IMO, I wouldn't be at all surprised if the coach's DD is catching when she's not pitching and pitching when she's not catching. Does your DD really want to invest the time and effort to become a real pitcher? If she does, you will want an assurance that she will be given the opportunity to earn pitching time. If not, fine, will the coach give her the opportunity to earn time at her preferred position(s)? Would DD be happy just playing first base? Your DD's and the coach's answers (and the faith that you have in his answers being honest) will give you a sense of whether its likely to be a good fit. Make sure you do your homework and check out the coach's track record/Daddyball tendencies with some current (and former) players' parents, other coaches, umpires etc.
Re the other option - where and how much playing time would your DD get and would that work for her? Definitely need to check w/ the 10U coach to see if the playing down/pitching option is really a viable option if that's DD's desire. IMO, as long as she gets playing time, she'll probably improve faster playing with the more skilled players.
It's good to have options. Just evaluate them carefully and make the best decision you can with the information you have.