Welcome to SR!
I'm sorry for what you are going through.
I am a recovering addict. When I was using, I was a totally different person, and my main concern was getting more dope. When I would come down from being high, think about how I was hurting the people that loved me, I would avoid those feelings by getting high again. It's a vicious cycle.
Jerect is right...we don't get into recovery until we really, really want it. Most of us don't get to that point until we face some harsh consequences...jail, being homeless, etc. There is way more to recovery than just quitting the dope. Recovery is all about learning to live life, and not pick up again.
My brain is pretty much the same as before my addiction (I think), but I still have thoughts of using when I get really stressed. Today, though, I know how to deal with those thoughts and they remain thoughts.
Addicts lie, and even if you catch him red-handed, he will probably still lie. With an addict you have to go by their ACTIONS, not their words. I talked, many, many times of getting clean, but continued to get high. When I finally chose recovery, I didn't say much...I showed I was recovering by my actions.
There is no answer as to whether your relationship is over. I would highly recommend, though, that you focus on yourself and your kids. There is nothing you can say or do that will make him want recovery....nothing.
There are some wonderful people here, who have been or are still going through similar situations. You may want to check out al-anon or nar-anon meetings...it will give you f2f support and help you understand the feelings your dealing with.
Hugs and prayers!
Amy