Yes, there is hope, Johnny, and no, there's nothing you can do (directly, anyway) to "fix" this. As men, this is the hardest part for us. I mean, you write well enough for me to be able to tell you're an educated, bright guy, so INTELLECTUALLY you know it, but it took me probably TWO MONTHS after my wife left our marriage for me to finally "get" that
I
CANNOT
CONTROL
THIS.
and
I
CANNOT
FIX
THIS.
For us "fixers," that's hard.
The best thing you can do is back WAY off, and work on being the best father you can be for your kids. I sincerely doubt she's being honest about there being somebody else, but that's something too that you cannot control.
Have you read DB or DR yet? That would be my first recommendation, plus Sandi2's list of "Do's and Don'ts" for you to work on.
In the meantime, no hugs/ILYs or "melty man". Be strong; your family needs a hero right now, and it ain't gonna be your wife anytime soon.