if regina was still trying to regain her magic in we are both, how was she able to subdue david to the wall and also was able to get the hat to work in "broken"?

ok but how did she do it? was emma touching her giving her temporary magic or something?

I'm not exactly sure. As David said she probably just got lucky. That or she was too nervous to focus and Emma's touch calmed her down a bit so she could focus on using her magic. But that's just my guess.

That too