Its hard realizing, and truly internalizing and processing, the damage we can do to those we love. Its really hard. And hard to realize that, when actively using, we are pretty much people that one should run from, not walk.
You're in very early abstinence. Its going to take time. Just keep doing the right thing and work on forgiving (not excusing) yourself. Your kids will see the effort you are putting in and in time will find their way back to you. But trust me, if you relapse, all that effort will be lost and they will be right back to completely distrusting you.
I'm an alcoholic and the child of one. One that was drunk every night for my entire life. He never admitted his problem, we weren't allowed to talk about it, and he never tried to get better. It would have meant the world to me if he had just tried. And after everything, I do still love him (although that is combined with a lot of pity). Your kids love you. You can do this!