I honestly think that the reason she came back is because she is scared and afraid of being alone and to not have you there to provide her with everything that you have so far. I believe she is doing this based on her own SELF interest because 1) she came begging and crying back to you (which I understand you were all too happy to oblige) and 2) she is STILL having doubts about you guys working out even though it was her decision to leave you then her decision to come back to you. I do not like the terms and matters of this situation. I can wholeheartedly agree that if some guy was there to swoop her off her feet, you would have never heard from her again. Obviously her fling fizzled out.
By all means, you can do whatever it takes to prove to her and show you you have changed. But there are two sides of the equation. If she doesn't or hasn't tried to change, why would the two of you conceivably work out? You weren't 100 percent of the problem and although you went great lengths and strides to become a better person and change, what has she done as well? She tried to erase you from her mind with somebody else and then came back to you when he wasn't meeting her needs. That leaves very little time for self reflection and change and all of her decisions were clearly made on an emotional whim.
I wish you the best but I urge you to really take this slow. I really believe your love for this woman is hurting you in a way as it has blinded you to everything before in the past. You guys are trying to mix having fun and being happy together with trying to fix and problem solve a broken relationship. You wouldn't pour gasoline on your pancakes for breakfast would you? Random analogy, I know.
Waking up next to a beautiful girl,
Step outside and say hello to my beautiful world.