She should, but unfortunately, "being a bad drunk" is one of those things people tend to gossip and eyeroll about (and then miss you out of events because of) rather than address directly. A great many of us have "embarrassing stories" from our pasts involving drink, especially as teens, which most people see as forgiveable - if not forgettable!! - but most grow out of it once we have responsibilities and drunk really isn't seen as "fun" anymore. Also, previous defensive reactions like "they're just being controlling"—which are incredibly common in people with problem drinking btw—may have been what's led to the more passive aggressive approach developing from those around you. Resistance is a powerful force, and yes, since it's a family pattern, is very likely to need help getting to the bottom of and changing.
My oldest friend (who I've known for 40 years now), whose father is/was an alcoholic, is also a massive pita when drunk although no karaoke or dancing on tables, thank goodness. Instead, it's either, if you're out, doing the grabbing you, practically strangling you to tell you she loves you, usually in front of people. but getting maudlin and self pitying about how you don't love her enough, or just phoning up and ranting for hours, talking over people etc, full narcissistic monologues, really heavy on the self pity, but no interest in you or what might have been going on for you that day. When not drinking, she's not like this at all.
I was passive about it for years, esp as I know she had a genuinely difficult upbringing, but I got to the point where I lost patience and now do not entertain it at all and cut the conversation short if I can tell she's been drinking, and tell her so. We have good times when she's not drinking, and she knows that, but I'm not prepared to put up with her when she is. Other people, you'll find, even friends who really care about you, will go for self-preservation rather than self-sacrifice; they're your friends and do care, but they're not your therapists and aren't responsible for fixing you. It's notable with my friend and the excuses about why she "had to' drink."I work so hard" (she does indeed, like her dad, and runs a successful business), but "I can't wind down any other way". Her husband and me and several others have tried over the years to get her to stop/seek help, but she always seems to find a reason not to or not to try, so setting boundaries is often all people around you can do.
Horrible as it undoubtedly feels, I'm really glad you've seen it as the wakeup call it is, OP. Both for yourself and your friendships and relationship, but for your babies too. I hope for all your sakes, especially theirs, you're able to break the family pattern - I know it's not easy. But it's clear that your friend does value you and your husband loves you, and since they feel that way DESPITE your behaviour and aren't enabling you, I'd say you've got a lot going for you and a good chance of being able to make the changes you need. Sorry for the giant essay, but please see this humiliating incident for what it is - and best of luck with the changes you need to make xx