It sounds like you're ok with things proceeding the way they are.. and possibly progressing.
She has already (actions are SO much more telling than words!) shown you that alcohol is more important than time with you, or the children, frankly. That she doesn't respect the intimate committment of your relationship as she gropes and makes out with other people. That she is not there for you physically, emotionally, spiritually or otherwise. You're having a relationship with an empty shell right now, and if she is an alcoholic, will only get worse. It's your choice to keep on this ride and watch as this all goes down, kinda sucks you're taking children along for the view..
I hope you find yourself, and possibly your children are worth more than this..
And to answer your question about whether or not she has a problem with alcohol... it's a problem for YOU, it's not a problem for HER. She has absolutely no reason to change what she's doing.. but you can change what YOU are doing.