I would question why she is wanting a longer glove - especially as a pitcher. Keeping it as light as possible with a good quality glove should be the emphasis. Nokona makes a kangaroo back glove that uses cowhide on the front and kangaroo on the back, so it's a nice trade off. Unless she's also playing outfield, I'd try to keep as small as possible. DD used an 11.5" Nokona from high school through college as a pitcher. But it really comes down to personal preference and what she's comfortable with. This is not a one-size-fits-all type of thing.
Be sure she is catching properly with a small lightweight glove, FITTED PROPERLY, with good padding. Remember, a pitcher catches the ball over a hundred times during a game, so it's possible her hand is hurting?
From day one with a glove, KEEP A BALL IN THE POCKET when the glove is in her bag. Use a good conditioner in the off season to treat the leather, put a ball in the pocket, and wrap/tie the pocket around the ball with a long shoe lace.
A good quality glove can be rebuilt many times and made like new if it's taken care of. I highly recommend Bretman for this challenge - he also has lots of great advice on how to properly care for a glove and make it last a lifetime.