If she was the horse for small children, she's probably "bomb proof," which also might make her rather insensitive to leg cues and people hauling on her mouth, unfortunately. She's had very inconsistent cues, so she might be confused. You'll have to make sure you're clear and consistent with your cues, to help her learn. And you'll likely have to be firm with her, though hopefully you can lighten up the cues over time.
Regarding the overflexing, I wonder if that was a case of you not releasing the pressure when the horse yielded its head (your trainer should have told you about that). Or perhaps the trainer had you do it too much. Also, when you're turning, you should use leg pressure as well (so if you're turning left, cue with your right leg). That should allow them to figure out the difference between flexing and turning.
Anyway, I agree with smrobs that it would be worth working on lateral flexion and other basics in a snaffle as well. Just make sure that once the horse starts to yield its head, you release the reins immediately. Ask for more over time, but always remember to release the reins. Hopefully you'll be able to lighten up your cues, though it will depend partly on her mouth, I guess.
I'd also work on leg cues, with the same goal.