He said he has four kids and thus this isn't just about him and his wife.If she has outright rejected you for 6 years straight, then who cares what you do? Does anything really matter?
What if you get caught? What's she going to do - cut you off??? Be mad at you?
She already hates you and has no feelings for you other than resentment and contempt.
Realistically will she even care? Will she even notice or is she so detached from you that she will simply be glad that you aren't around as much and aren't bugging her for sex anymore?
Would she divorce you if she finds out? Would you really care if she did?
Or would she be relieved that you are parking your boner somewhere else and she'll want you to keep paying the bills and rent?
Your marriage is already dead in the water, she already hates you and thinks you're an A-hole. What happens if you cheat and get caught - - she'll think you're more of an A-hole???
I mean what does she care? she doesn't want to touch you anyway and it's not like your going to give her herpes or anything.
And if this is what is need to push one of you over the edge to grow some balls/ovaries and finally get a divorce, then I say go for it.
What if his kids find out? Is this the type of man he wants to show his kids that he is?
What if he got the other woman pregnant?
What if the OW husband found out and started banging on his door to confront him in front of his kids?
What if his wife found out and started telling his parents, his sibs, his friends, people at work?
His wife is dug in on the no sex. If he's a man of character and a good father, he does one of two things. Either gets into counseling with his wife to address her comments of he's "not been nice to her", to see if this may change things, and if it doesn't then he either accepts that being in a no sex marriage is just the way it is OR he ends the marriage because he wants to have a marriage with intimacy.
He has to look at himself in the mirror and like who and what he is and the decisions he makes. He does NOT do what cowards do and that's sneaking around and cheating not just on his wife but risking blowing up his kids world.
OP, all this OW was doing is fishing to see if there's a crink in your marriage and if there is she could start to share what's wrong with her marriage as well and the two of you start to get close to one another and you know where this heads.
How much longer do you think you can go in a sexless marriage? Do what you have to do to "try" and fix it and if after doing this (counseling) you find that it's not you have a major decision to make.
Our lives are about the choices we make. Don't choose to be a coward and cheat on your wife even if it's sexless. Your wife finds out you cheated and she divorces you trust me your kids are going to blame you for their family being blown up.
If you get into counseling, and things don't change, yes you could still divorce, and as far as your kids are concerned it will be about other issues NOT that you cheated on their mom.
Choose wisely how you move forward.