Hi Floggo...WELCOME TO SR! I'm glad you found this place. There's much Experience, Strength and Hope (ESH) to be had here.
From reading your post, I can understand why you are questioning your relationship with your RABF (recovering alcoholic bf). The whole "I can't live without you" crap is VERY stressful. My XAH used to give me that all the time, putting all this pressure on me to "be the one who saves him". I tried to play that role for 5 years and then it became too much for me.
I also have a 2 year old DD, and SHE's the reason I left. I could not have her growing up in a toxic household with an alcoholic father.
Perhaps your hesitation with regards to ending the relationship have to do with the fact that your BF is in recovery...others from the board will soon be along to confirm the fact that just because he's sober doesn't make him a perfect, or even a decent partner. Sobriety doesn't ensure that inherent character flaws are suddenly erased.