Hi Kate! Glad you came back.
Sometimes people can get caught up in the dissection of "what went wrong" and find themselves staying in situations trying to put the puzzle pieces together. While I understand why you look for cans, or try to figure out how he is getting money to drink, neither of the actions is helping you in anyway. In fact they are harming you. There is no need to question him anymore over IF or WHY he is drinking. He IS drinking. He IS alcoholic. He is NOT stopping. Counting his cans or do anything to monitor his alcohol consumption are detrimental to YOU. Why? Because even though you have a long history here of him lying, and breaking promises to stop, disregarding your request to not drink at the home you STILL question whether or not "this time" he has stopped. This will make you crazy - you already know the answer.
The uncertainty kills me more than knowing. This has kept many a person in a relationship too long. You ABF has played many mind games with you to the point that you might question is drinking if you caught him with a beer in his hand. When my husband relapsed he showed up at our home with a drink in hand and so drunk he could barely stand, yet told me I was crazy for thinking he has been drinking. Stop participating in the game - you know what you know. This situation is NOT changing.
As far as your animal, animals like people do not do well in tense or abusive situations. You are at the point in this relationship that medication has been suggested for you in order to stay, that's about as bad as it can be. Small steps are what it takes and coming here was a first. Try and stop looking for cans, try and stop asking him about his drinking. These are the first steps to detach from him and not be joined at the hip in his alcoholism. Start daily to work on your exit plan.
Its so ironic we all get wrapped up in the "what if" I leave and concern about what will happen to the alcoholic. The alcoholic in your life could care less about your mental health and for that matter I doubt cares much about the health of your animal. He cares about drinking, and little if anything else. Move forward and do what's best for you and your dog and try to make yourself a priority!