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Not that uncommon for a travel ball player to play on a REC team to be with friends. Also not uncommon for her to be one of the better players and likely a pitcher on the REC team even if she doesn't pitch for her travel team. Let the kid play and pitch, but I would be sharing innings with other pitchers on the team, not pitching one kid only. Teach them all to play mutiple positions. IME her making all REC activities that don't conflict with travel team, might mean she's there more than some of the kids who only play REC ball (i.e. there will be lots of kids missing games for lots of reasons at REC level). If you want to be part of a team that penalizes kids for missing practices and team events, play travel, otherwise let this kid get as much enjoyment as she can from playing with her buddies.
When I coached REC my policy was pretty simple you played an equal amount of the time you were there. If you miss a game I won't play you more the next game to make up for it, but you'll share time with the other kids that show up that game. So in the situation above if the the travel girl makes it to 1/2 the games and there are three pitchers I would think it reasonably fair for the travel girl to pitch about 1/3 of the time at the games she makes it to.
This is pretty close to what I do. I keep a spreadsheet on who played when and where. I have a column for "Absent" and count that.
The only consideration I place on missing practices and games (in REC) is a player not knowing what to do during the game. If you miss a bunch and don't know when to cover a base I won't put you there and I'll gently tell the player that I'll give her more time there when she has picked that knowledge up. I may put here there later in the game "depending" but that is up to the game.
As far as pitching I'd agree with the above that she is considered 1/3 of the staff but I probably wouldn't make her the star and give her most of the innings. You DO have to have an incentive for coming to practice and games, with the reason for not doing so in mind. I have had players miss due to other valid commitments and I've had players miss just because the parents are too sorry to bring their kid. Is it the kids fault? Usually not but part of playing a sport is being taught some responsibility by the coaches so I try to work that all in with the knowledge that it is a rec league.