Hey Ben- my fiance is a drinker as well, though I haven't faced some of the same relationship troubles. She drinks enough that I worry for her health, but she's pretty steady about things. No cheating or craziness- I went through that with my first wife.
In my first stretch of sobriety while my girlfriend and I have been together, it was a bit rough. She wanted me to be able to have a drink with her, she didn't want me to "expect her to stop drinking", etc. It took a while, but she understands now and is supportive. It will change your relationship, hopefully for the better. It takes patience and a lot of courage to open up. Just admitting to having a problem drinking for me and trying to quit can be tough.
Some of the best advice I've received on here is that staying sober is an inside job. Ultimately, we have to want it and do all the work ourselves. No amount of support or lack of it can make you or I stay sober. Not that support doesn't help, but I learned to not use other people as excuses. Even if your relationship doesn't work out, and maybe you don't want it too, staying sober is number one.