You have already gotten some great advice. Alanon was a huge help for me in dealing with my husband's drinking. If a meeting seems scary or it feels too soon, you could always start by reading some alanon books at home (many libraries have them). Live meetings are awesome and I love going, but I remember how chicken I was at the start.
The main thing is TAKE CARE OF YOU! I know this sounds so foreign and so hard. We are so used to looking after our alcoholic/drinker that we feel way too busy, responsible, stressed, whatever...to do what feels good to us. I know I always thought, "if I do not fix this problem, who will?" or "if I do not fix this and make our marriage better, who will?" And the answer is, I don't know. Maybe it will get fixed, maybe it won't. God has a plan and I do not know what it is.
But I have learned (and I really hope you do too) that it is not my job or duty as a wife to FIX my husband. I spent years taking on tremendous responsibility for the success (or failure) of our marriage. If you feel like the drinking is a problem, it is. Take care of you. Looking through gym bags is a sad sad way to live your life. Did you ever think you would wake up one morning and think "how do I want to spend my day? Oh I know, snooping through my husband's bags and things to see if he has been drinking". It says a lot about your husband. But it also says a lot about you. that you are choosing to spend your precious days in this way. I am so sorry if I sound harsh. But I wasted a lot of my own precious days doing the snooping, nagging, arguing, convincing, talking. I hate to think of others joining the grips of the disease by losing themselves. Please start spending your time in ways that bring you peace - not anxiety, stress, anger. Everything will work out as it should - your only job is to take care of you in the best way you can.
One more thing about DENIAL: You mentioned your husband admitted he had a problem, quit, then tried the "a few beers" thing. Mine did the same thing, a few times. It sounds like its not a true admission and, obviously, not a real recovery. The Alcoholics often believe what they say at the time, but it is really their disease lying/manipulating you to get off their back. Unless you see a commitment to recovery, he is still drinking. Do not be surprised. Do not snoop. You can assume he is drinking.
Now, what are you going to do with your time and your days. Once your eyes have been opened to the problem, the best thing you can do is look to yourself. Stop looking at the alcoholic and his drinking habits. Look at yourself and what makes you happy, joyful, peaceful, calm. The ONLY thing you can attempt to change is yourself. Believe me, I wasted so much time trying to change my husband, to get him to see the light, to convince him to fix his problem, fix our family. I changed me, started spending my days seeking out peace, and I am happy now.
God Bless and good luck to you! Welcome Welcome Welcome. You will find support here. I am thinking of you and wishing you all the best.