I am never a fan of a travel ball coach giving his/her own players lessons for money. It is just is a good way to invite feelings of favoritism.
As far as whether a coach should teach hitting during practice. That can be a touchy subject. They definitely need hitting reps in practice. As pattar said almost every player has their own hitting instructor but I do think there is room for some minor corrections and definitely lots of encouragement.
If your coach is only doing fielding in practice and telling you to come to their private lessons than I would have concerns.
As far as whether a coach should teach hitting during practice. That can be a touchy subject. They definitely need hitting reps in practice. As pattar said almost every player has their own hitting instructor but I do think there is room for some minor corrections and definitely lots of encouragement.
If your coach is only doing fielding in practice and telling you to come to their private lessons than I would have concerns.