Hi stepping up,
My AH and I have had many tiffs around the subject of chastising our daughters (when they were younger). My AH generally complained that I did not always back him up, but sometimes I didnt agree with him or his parenting skills, so I didnt and would generally walk away or not say anything. Later I would just say 'I thought you were handling it, so didnt need me to jump in'.
My AH has not been consistant at all in his parenting style or skills and sometimes he has left me feeling aghast at what he has said or was doing that there was no way that I was going to join in. The key phrase here is 'agree to disagree'. You dont have to agree on everything in life and if there is something that you cant agree on, that isnt a deal breaker, then let it go and move on.
I undertand the principals of standing together as adults, one united front, as kids are very clever at playing one parent off against the other. It sounds like your son has found the 'angle' to divide and conquere, so I would suggest that you and your wife work out a compromise to tackle this before it gets out of hand as it sounds like a slippy slope (if you want to stay married that is). I know its easier said than done when dealing with an alcoholic who is not always consistant in their responses, its a tough balancing act.
I would suggest that these family disagreements are extremely common and happening all over the world, our circumstances are just complicating matters. There are some good books at the library about rearing children, especially 'clever' teenagers, so maybe start there and that way, you can open up the lines of discussion with your wife about which way to handle your son and his grades etc.