Having been a person on the receiving end of my husband cheating with another woman, my sympathy goes to your wife.. and your children as well..
So I think for their sake you should think seriously what's the best for them;
I believe that other woman is just a person you went to cos you were scared of being on your own;
If you tell her gently it's over , you really want to make a go of it with your children , you love and miss them.. and want to move closer to them..
Thank her for being there for you when u needed someone... but it has to be over .. one of the hardest things you ever had to do in your life..
Maybe you could tell your wife you'd deal with your problem the right way,
by moving to a closer place where you can see your children more often..
and you could try & Re - Romance your wife.. ??
Do all the things you know she used to like when you were dating..
and see if you can rekindle the spark that you've lost..
That way you can say you did all you could to save your marriage..
If it doesn't work .. so be it.. Move On..
I tried that with my husband
but he was too far gone with the other woman..
My children were all grown up when it happened
so they're not affected quite the same way as yours .. one lives overseas ..
but it was still a shock for me.
I wish you luck in your endevour,
It's going to be interesting to see how it goes..
All the Best.. belle.x