Op, legally, don't worry, your mother/the ow can't sue you for libel if you can prove what you said was true (correct me if I'm wrong legal types, but I believe she'd need a copy of that letter as well, good luck to her getting the wife to hand it over!!) She can't say you are harassing her if you wrote a letter to someone else.
So on that front, relax. Let her waste her money on a solicitor, they'll tell her the same thing for a big bill.
As for what you did, if the op came on here and said "my mum had an affair and that broke up my patents marriage. I've found out she's now having a relationship with another married man, they are both quite open about it so lots of people know, but the mm's dw doesn't know. I was thinking of writing her a letter telling her because someone should tell her, it's unfair she's the only one who doesn't know. I'm going to tell my mum I'll do this so the mm has chance to come clean himself, do you think that's the best option?"
Then the op would get 10 pages of "I'd like to know" and "being in an open relationship is fine, but only if all members have consented to it, unfair if the wife is the only one who doesn't know". Then "well you have them a chance to tell, you should tell the wife".
Personally, I think a call would have been better than a letter, but that's done now. Disengage.