Hi there. Wow, you have a lot going on.
Congratulations on your own sobriety. Protect that at all costs.
Your wife clearly has a problem. Call it addiction, alcoholism, it really does not matter. What matters is her actions.
You call the things she is doing "slips." I would hedge to disagree as I am betting you only know the tip of the iceberg. My concern would definitely be for your children first. Their safety. Her drinking then picking him up from a lesson? Unacceptable. I know it may take some doing, but until she can prove herself sober, long term, I would not let her drive those children no matter what.
You cannot love her sober, nor can you be responsible for keeping her sober. The three C's are: You did not Cause it, you cannot Control it, and you cannot Cure it. It's her decision. I would say to do what you have been doing, try to be open and honest with her, and step back and let her decide if she is going to be sober, or not. In the mean time, hope and pray for the best, prepare for the worst.
I say all of this kindly as I know it's painful. Keep reading, keep posting, you are not alone.