If they're saying they'll 'consider' it but they're not rushing to give you the confirmation you want, I'd say they're not feeling entirely comfortable with the situation. If social services were of the mind that your boyfriend moving back in would result in a happy and harmonious environment that your children could thrive in, would they possibly give a more conclusive answer?
If I were you, I wouldn't continue pursuing living with this man. Creating this mess for himself is bad enough, but then failing to comply later on doesn't bode well either. Of course, there's a chance he could completely reform. But his lack of compliance in the first place would leave me feeling as though I wouldn't want to set my children up for that particular experiment. Children need consistency and dependable role models. If this person has flitted in and out of their lives because of his actions, they're going to feel anxious if he's allowed to return to it on a full-time basis.
Walk away from this now and save yourself the hassle of feeling anxious and scared. I'm guessing these proceedings are causing you to worry? Enough to post about it anyway! It sounds as though you've put your fair share of effort in with the courses, but he hasn't done the same. Does it seem as though he's worth taking a risk for? Or, is it better to release yourself from the drama and open yourself up to one of the many, many kind and loving people who exist on this Earth?
I can't say I understand your rationale for pursuing this relationship. However, I have found myself in far less troubling scenarios where I've been reluctant to cut myself off because it would feel like I had somehow wasted years of my life. Trust me when I say that your current situation falls well into the category of "It's never too late to undo a mistake." I'm sure both you and your children deserve better than this.
(FYI: Not old. Also, some of the BEST advice I've had on relationships has come from my Nan).