Really, if he is not continuing his recovery process, he is NOT doing eveything he can to strengthen your M or become a better father.
As someone already mentioned, addicts are never cured, and recovery is lifelong.
Does he have a CSAT?
Is he in a 12 step group?
Does he have a sponsor?
Has he worked the 12 steps?
Is he even sober?
Heck, step 9 is making amends, so I'm going to guess that he'd need to do a healthy portion of that with you, so you'd likely know it if he ever got to step 9.
We've been on the long road of R with SA for about 5 years. I did IC with a CSAT who specializes in working with spouses, H sees his CSAT once or twice a month, we see a CSAT MC once or twice a month.
It is a long road. I'm pretty sure the 2-5 year statistic you hear about R does NOT include addicts in the computation.
It takes 2 healthy people to have a healthy M, and an addict has a lot of work to do to just get to the starting line.
Living with an addict can cause trauma and/or codependent behaviors in the spouse. You need to find stability on your on for yourself.
Then, the M can be addressed.
My H started after dday with a garden variety IC who had no clue how to identify or treat SA. Then he had another quite similar one. Two and a half years wasted - oh but those guys were covered by our insurance - so that seemed like the "smart"" path to take. Not so much.
So dday was in Spring of 2006, but H didn't even begin recovery till summer of 2008. And it will be a lifelong journey.