Spot on.
Not enough emphasis is placed on the fact that once a man beds a married woman, for whatever reason, he has shown his true moral colours. He is demonstrating that he is a sneak, willing to secretly trash the standards of everyone else to get what he wants. He knows and understands the ‘wrongness’ of what he is doing and that is why he is surreptitious in his behaviour. If he is like that on this occasion, then he will behave in a similar fashion on other occasions. It is a part of his character. He is not someone who can ever be trusted. Sadly, he has bought the OP down to his level.
If, as you say, your husband is a ‘good father’, then that’s how the kids will know him. If you walk out, you either take the kids, or leave them. If you take them, they will spend the rest of their lives wondering whay it was that their mother suddenly decided that their Dad wasn’t good enough to live. Their notion of what a good father is will be rocked to the core. It will never make sense to them. Ever. You can’t say to them you don’t love your husband, their Dad, because that would be a lie. So what would you tell them? That you want better sex? Wow, what a horrible message and lesson that would be for the kids, which is, you can dump someone because you can get better sex. The fact that Daddy is a good person and a good parent doesn’t really matter. Now that’s a perfect way in which to totally screw up your children’s value system, isn’t it?
If you leave the kids behind, you will be destroying their faith in you. You will be someone who can’t ever be trusted again, because you are a danger to how they feel emotionally. You will hurt them terribly, destroy their faith in you and destroy their faith in the security which is the family they are growing up in. The hurt will be so profound that they will not, ever, be able to trust you 100% ever again.
The pain you cause them will affect them for the rest of their lives. The ability to trust, to love unconditionally, to feel safe and secure in the knowledge that your parents are always there for you, together, will be destroyed. It will affect their future relationships with others, because the stability, the unstated promise of future unconditional love and support will have been destroyed. It is the kids who will be the real victims and their children as well, because the role modelling of a stable family and safe, unconditional love, will have been denied them.
Your husband will be rocked to the very core of his being. He will feel violated and betrayed beyond comprehension. It will affect his entire life, because even he, will struggle to know what is real and what is false. You say here that you love him. It is therefore reasonable to assume that you still tell him you love him. If you now break up the marriage and the family, he will never make sense of why someone who supposedly loves him would want to walk out. How could he even be asked to make sense of it? It will haunt him for the rest of his life and it will affect his relationship with the children too. They will all have to suffer incredible emotional and spiritual pain.
And all for what? So you can have better sex? Is better sex more important than the emotional well being of your own children? Is it worth more than the ability of your husband to be a loyal and loving father to your children? Is it more important than watching your children grow up feeling safe and secure in the bosom of a loving family? Is it more important than being able to give your children a childhood they can look back on and be thankful for? Is it more important than being with someone who is obviously unconditionally committed to you and your children?
You wrote that “My spouse and I have always had some sexual incompatibility issues”. Is that the ‘excuse’ for contemplating breaking up your own family and destroying the happiness of your children and husband? Is that the excuse for accepting the advances of a man who is willing to demonstrate a total lack of respect for your own family and for your position in it? For a man who doesn’t care about how important your role is in the safe and stable upbringing of your children?
Just as Luvtosew wrote, you are walking into a big patch of weeds and abandoning the green grass that is your children’s and husband’s unconditional love.
The choice should be fairly easy. You just need to find the ourage to admit it and the self respect required to make the acknowledgement. Settling for weeds is just another step towards destroying yourself as well. Get rid of the what is causing you to be depressed and confused and have the courage to keep your little bit of pain to yourself for the sake of your family. The alternative will be horrendous by comparison.