Seasoning a mare and she is figuring out her style. She wants to run straight in and pivot on the backside. I currently ride in a short shank smooth mouth dog bone with 1" of gag and a loose curb chain. I feel like I need more support to help keep her straight up going into and out of the turn. Not to lift her off of it, but to just keep her straight up. She's very broke and soft in the mouth so I'm staying away from long shank. I was thinking less gag and a more solid mouthpiece for stability?  

Tighten the curb on what you're riding. That may make a big difference.

I like the Pozzi short shank hackamore to keep one straight but I prefer hacks over bits anyway and her hack is very universal.

Can Can was spot on with tightening the curb.  It will reduce the gag action.