I'm in therapy and it's helping

Good!

I'm struggling at the loss of it all and even though we've been out the relationship 9 months

This is normal. It would probably take many people 9 months or more to feel better about the loss of a 10 year relationship + kids. You have to see her on a regular basis, so you don't have the benefit of going no contact to help yourself heal, and you don't seem to know how to cope with negative emotions well. You are going to feel like shit for a while and it sucks.

You probably feel like you can't stop yourself form begging her to take you back because when you see her, you are completely overwhelmed with emotions. You are scrambling to make the bad feelings stop, in that moment, at any cost. Please take me back! Please make the pain stop! You have to learn how to recognize and tolerate those negative emotions in order to give yourself a second to remember that:

I just want to leave her alone and recover... I want to stop, leave her alone and focus on the kids.

The pain is normal. In order to do what I quoted above, you have to experience it. Trust that it will fade eventually. Talk to your therapist about working on identifying emotions, and learning how to tolerate them and react appropriately in the moment.

Knowing I caused all this with my moods and horrible temper kills me inside and I'm struggling to move on.

If you really, truly feel like you're a "broken" or "bad" or "horrible" person inside, there's therapy to heal your core beliefs, too. Liking yourself is pretty key to making good decisions and enjoying life. It's hard work but incredibly worth it.

You're in a good place to change because it sounds like you want to, and not just in a frantic attempt to win her back. Good luck in therapy.