My mom is finally trying to get sober

My mom, after over 40 years is finally stopping drinking. She had some major health issues come up and she said that she hasn’t been drinking for a week. I’m very proud of her but at the same time I’m suspicious. As far as I know she isn’t having any major symptoms of withdrawal and as glad as I am that she isn’t suffering it makes it hard for me to believe. I’m being told by my step dad that there’s no alcohol in the house for her to drink and she doesn’t drive anywhere for her to get it herself so I believe him. I’ve been having major anxiety over this situation for a week now. My husband doesn’t want the kids around her which I can understand because they’ve had minimal contact with her because of her drinking but now that she’s having health issues from drinking I don’t want my kids watching that. The issue I have is that if she really is being sober why am I keeping my kids from her. Isn’t that going to hurt her and make her want to drink? They are his kids as much as they are mine so I don’t want to not give him a say but I just don’t know what’s the right move.