As was told to me (about this very subject) from wise folks with more (codie) recovery under their belt than I - don't have The Talk with her.
Have it with you.
YOU are the one that needs to hear the list:
I've got a problem with her drinking.
I'm going to get help.
I'm going to let the kids know that there's help for them.
I'm not going to engage with her or let the kids engage with her when she's drinking.
I'm going to tell the kids to stay away from her if she's drinking and I'm not home.
I hope that she chooses to get help too.
So, go get help.
Talk to the kids.
Don't engage when she's drinking.
And remind yourself that your recovery is for you.
It may sound like crazy talk, but nothing needs to be said.
Now, that is not to say if she is doing something unacceptable, you can't tell her "no". It's just to say that she knows you don't like her drinking and she can't or won't change.
The work is for you to take care of yourself and your kids now.
She will get the gist and you grow in your recovery.
Hugs and peace