Some common sense points:
- If all you have with him is a spoken agreement, then your contract is worth only the paper it is printed on. To wit, you have no legal legs to stand on. If you do have papers, that's a different story.
- Do not involve his wife. She's not his boss and you don't work for her. That was highly unprofessional of you.
- I think he's not wrong to gig you for the wasted time and materials it took to undo the damage you did. It's a matter of whether the time and money it took for him to fix the damage was equal to or more than what you are usually paid. If it was more, be glad he didn't bill you for the difference. If it was less, you have a right to what's owed you - no more.
- Knowing that he's a handyman whose job is to refurb rental units and that includes all manner of plumbing, why in the world did you not check the pipes under the sink first? Or at least ask? Sure, he has a responsibility to keep you apprised, but considering the context you have an equal responsibility to confirm readiness for use. You share blame equally on this point.
- And why the heck were you dumping a bucket in the sink in the first place? That was just daft. You dump buckets in the toilet. It has much larger pipes and is virtually impervious to clogging from whatever might come out of your bucket, short of wads of dog hair and rags.
- Don't be surprised if he never needs your services again. Bringing his personal life (getting his wife on your side) into his professional life is an unnecessary and underhanded thing to do. Now you're a proven liability and destabilizing influence, and it would be completely reasonable for him to leave you out of any future work.