That doesn't seem to work.
Whenever I try pickpocketing the gold back it won't let me.
are you trying to do it right after traing or are you leaving the cell? if you leave the cell the money will be gone, just like if she was a merchant.
here is what to do
1. train with her one time (raise one level), exit
2. pickpocket the gold back (raise one level)
3. rinse and repeat until you are out of training sessions for you current level, return to her when you level up again.
Do not try and take all the gold back at once she will catch you every time.