You can definitely do this, for you and for your kids. Getting in to see your doctor is a great first step, have them help you with the anxiety management.
What did you do after rehab in the past to help you stay sober? Are you home with your kiddos all day long? Are you able to schedule any time for you? That is important for recoverynas well, even just a short walk, or a class, bath, something just for you.