Dictating terms is a tricky business...
when confronted with difficult relationship issues, weather poly issues or otherwise the first thing I like to do is try to really understand the other persons' perspective. If I can get my mind wrapped around what's motivating their behaviors or dialogue I can then begin to work towards a solution. I can say from personal experience though, once someone begins making demands in a relationship it's a slippery slope.
you are left with two choices; accede to the demand or refuse. Each has perils that must be weighed carefully. If you give in you cause resentment within yourself for allowing this person to control your actions. If you don't they wind up hurt because you're not putting a premium on their feelings. Having said all that in my mind there has to be MUTUAL consideration here. And that includes your BF. He does after all have a stake in the decision process. To look at it otherwise would be tantamount to relegating him to second class status. Compromise and work are the only real solutions. In these types of situations my gut instinct is to examine all possible paths and mutually decide what's the best path to get us from where we are to where we want to be. often times in order to accomplish that it's neccessary to minimize external distractions. In your situation it may well mean putting external relationships on hold for a little while as you work on the larger problems.
If you feel drinking to excess is a part of it you need to make that an issue. Not saying something is the same as telling a lie. letting destructive behavior slide will always end in heart ache and for what it's worth I've seen it play out first hand. The long and short there is if his drinking is causing you distress it's a problem, regardless of his opinion in the matter.
What it all really boils down to is that you sound like there are multiple problems here. Isolate the smaller ones and work them out and work up to the larger ones. Often times by the time you get to the biggies you find that they are little more than the accumulation of smaller stuff. I hope this helps, and if it doesn't, well, at least you got your money's worth lol.