It is often easy to flame someone for having an affair, brand them a bad person etc.
The truth is that affairs are never black and white. There are all sorts of reasons why people do end up having affairs, and sexless relationships are probably more common a reason than many others.
But, while affairs can often be explained, and while issues from the other party can lead someone into a position where they do embark on an affair, it is never a justification for doing so.
Nobody should have to live in a sexless relationship, and if this makes you unhappy to the point where you feel you need to seek sex elsewhere then you need to discuss it with your dh rather than go behind his back and seek emotional and physical gratification with someone else.
Because while at the moment you say your marriage is happy, for your dh, it is built on dishonesty and deceit.
If you were both happy in a sexless marriage where there was no expectation of physical contact and your dh was aware that you were in a sexual relationship with someone else that would be one thing. It may not be conventional but as long as all parties are aware and in agreement it’s perfectly ok.
However the situation you are now in means that your current marriage is completely unbalanced. Because your dh believes that you are happy together, that the relationship is working fine the way it is, what he is not aware of is that you have checked out of a part of the marriage in favour of someone else. In fact the fact you said in your op that if he found out it would be over says exactly why what you are currently doing is not and can never be ok or justified.
And ask yourself this. You say you don’t want your children to grow up with stepparents, can you not see that you are projecting your own childhood experiences on to them? Whereas if you live this life they will have their own childhood experiences to project on to their children one day – that they wouldn’t want their children growing up in a house where their mother had a bloke on the side and their dad was oblivious, and they knew but she didn’t know they knew and they felt caught in the middle between the responsibility of telling their father and the loyalty to their mother.
And what of the OM? Does he not have more self worth than to be someone’s bit on the side for the foreseeable future? One day he will want a stable relationship of his own, and how will you feel then once he moves on?
I am not judging the affair. We’re all human and these things do happen.
But you cannot arrogantly retain control of everyone else’s life just so that you can live the life that you want. The other people in your life have a say in how they live their own lives, you may be the master of your own destiny but you are not the master of theirs.
If you want to stay in your marriage then you need to speak to your husband about what needs to change. If change is impossible then you need to think about how to end the relationship in order that you all be allowed to move on and find your own happiness. And that includes your dh.