You seem to be doing everything you feel like you can do. It is a journey I think. One that may get worse before it gets better. Ultimately staying sober is up to her. You've given her so much love and support but your kids also need that love and support. Sounds like you are doing the best you can which is all you can do. Letting her do this or that isn't the point. If it comes to that, then you cross that bridge but for now just let her do what it is she has to, either it works or doesn't but save your strength and worry for the kids.
I understand alcohol is an addiction and being a mom is stressful but you know what? I work with impoverished moms with lots of kids and they are all sober, loving their kids and being great moms. She is simply an alcoholic. Has NOTHING to do with the stress of parenting, she just had very poor coping skills for that stress.
The kids need you. Make them your focus, not her. Maybe this sounds harsh but it is their life that you can still fix and help, hers.. well she is an adult.