I have been reading articles on reason not to take back a cheater and in all of them they'd say that if H really loved us they wouldn't cheat.

I'm starting to believe it. You need to keep the course of your journey. I have a dog myself so I can easily relate to you, but remind yourself that you have no control in what is happening. It's out of our hands. Apparently some cheater never feel remorse, so you need to see it as being their lose to loose such an amazing woman. :-)