I've gone off sex in the past and then got more into it. You need a clear, open discussion together. You might need to see a counsellor.
What you need to work out really, or rather your wife needs to work out, is whether
your wife has gone off sex full stop
gone off sex with you
and whether she can find her way back to enjoying sex again or whether she doesn't really want to try that.
Then when you are clear what the future holds you can discuss together the way forward.
I don't think an affair is a great idea, even with your wife's 'consent' you would be hooking up with another woman who may well develop feelings for you and you for her. But whether you go down this route is up to you both.
As a heterosexual woman I must say that sometimes our sex drive can be very dependent on our feelings. Or is that just me?
So for me if my husband pisses me off with a thoughtless comment or anything event remotely annoying then that can be a passion killer.
For me this is not about how much housework he does, or how much he earns. It is about how he makes me feel.
But if your wife has gone off sex, then no matter how nice you make her feel you may find she does not want to have sex.
She may even feel scared of sex. I have not read all your posts, could she be scared of getting pregnant again?
Could she have some form of post natal depression?
Honestly, this problem may be more common than you think.
You are not unreasonable to want sex with your wife and you are right that this may well eat up your relationship, from the inside out. But she is not obliged to have sex with you, no matter what you do about the house, and you are not obliged to stay together (IMHO).
Good luck. 