Seems anxiety and substance abuse go hand in hand. I have both (87 days sober).
Anxiety can only be dealt with when we have a clear head. So first and foremost is get a couple sober days under your belt.
Most of my anxiety had to do with fear of things out of control. I listed all the things that caused me the most grief and addressed each of them one at a time. Approaching them in small bites gave me a sense of traction and I could move forward addressing the others. As the list got smaller so did my desire to drink (not completely). Some things on the list I have no control over and I had to just accept.
Anxiety and addiction both take action to overcome. Asking for help is essential (you just did). You may need medical assistance for both. Start with a very frank discussion with your Dr.
Choose to get off the hamster wheel. "I drink because of my anxiety, which makes me more anxious, so I drink to deal with my anxiety, which makes me anxious, so I... " You get it.
Being there as a great mom for your kids is a great motivator. I wish you success.