I'm really sorry to read your story. I know from experience that I thought my anxiety meds didn't work either. It is only when I stop drinking that I feel better. I know that drinking affects the meds so they don't work and drinking makes me even more depressed and anxious.
I have a child although older and know how hard it can be when they are young. Seriously, it is so much easier when sober. There are people on here who have lost custody of their children because of drinking so please take it seriously. It can and does happen to people who really wouldn't expect it.
Have you tried AA or got other f2f support? What did you used last time to get and stay sober? Can you do that again. Maybe AVRT or SMART. You're obviosuly under such a lot of pressure and need help. Can you put the kids in nursery 1 afternoon/day and get to meetings or something.
I wish you well.