Garden and pines;
I know I sound like a broken record sometimes,
but I truly believe you can rebuild your relationship with your children
by staying sober for good and building a solid recovery foundation--not just not drinking.
Show them who you are sober, and they will, over time, want to know the "real" you.
When you grow up with an alcoholic parent, trust doesn't come easy as betrayal and lack of emotional safety are the rule, not the exception.
Unfortunately, my mother never managed to stay sober, and her lapses
made it harder and harder for me to ever have faith I could be close to her.
Yet she always expected me to engage with her emotionally even after brief periods of sobriety,
and she would be upset and angry when I was unable (and later unwilling) to do so.
Don't make the same mistake she did.
This is why you have to be patient and not push your kids--
show them you are trustworthy over time by working on healing yourself.
Staying sober no matter what is the critical first step of this process.
If you are willing enough, and work enough, the rest will fall into place.