The Rawlings HOH is a great glove. The difference between baseball glove and softball glove is a softball glove tends to have smaller fingers and a bigger pocket.
http://www.heybucket.com/viewtopic.php?f=2&t=73523&start=20Smaller pocket is going to make for much quick transition. If you have the skills you can definitely play with a smaller glove. It is common at upper levels of college ball to see middle infielders with smaller pockets.
As far as the overthrows, and a glove change making a difference, someone would have to see the nature of the overthrows. I mean if they were way offline, then ignore dad's helpful commentary. If they were pretty close, and your daughter might of had a better chance with a bigger glove, you might try an 11.75. I would definitely not get talked into the anything bigger based on what I am hearing.. You having been there are going to be in a much better position to make that judgement.