I'm so sorry, rubyloo. But you are NOT inadequate. It isn't anything you did or didn't do. Your DH is trying to prove something to himself and to the world. I think often, that sex is only one part of it and that partners who have affairs are trying to conquer something else, like getting older.
In the culture and community I grew up in, it has been acceptable practice for husbands to have affairs and keep mistresses. Within my extended family, this has happened too. Sometimes, the wives leave. Mostly, they stay, not just because of the children but because they love their husbands.
Whenever we hear of another affair, quite a few of my girlfriends say, "If that happened to me, I'd leave". It is naive and too simplistic. I feel for you because I've seen how affairs can wreck lives and how the wronged partners blame themselves. But I've also known marriages and families that have picked up the pieces and healed again.
rubyloo, the trust will be a long time coming but if you feel you want to give your DH another chance, do it. Not just for your children but equally importantly, for you.
Take good care of yourself. {{{{{{{hugs}}}}}}}}