two things:
-sitting down with her pre-emptively strikes me as a really bad idea. it smacks of assuming ahead of time you know stuff. or are warning her about things that she hasn't done.
if i were an employee who got sat down that way by my new supervisor i'd feel only condescendingly treated and judged before i had even started working "under" them. it would be a real bad start for me. undermining.
-secondly, you've had those phonecalls. she may or may not be an alcoholic. has nothing to do with her making phonecalls to you when inebriated. my suggestion would be to spend some time thinking about your own boundaries about this, instead of about expectations about her. if you're clear on what is and isn't okay with you, you can communicate that clearly when/if the situations comes up again.