I am so sorry you are going through this.  These people have a way of creating a psychological hell that is incomprehensible other than to those of us who have also been through it.

You know you need to leave, and it's the only way forward.  You can't stay inside a burning house.  Walk out that front door, and start picking up the pieces.  I'd start by hiring a divorce attorney to help you plot the way forward.

As for your statement "why do I keep holding onto the hope that he will choose me and our family", I was there, too.  My ex-wife was in an affair with the mother of our older daughter's best friend, and I thought there was some way I could fix the situation and save the family and my marriage.  The simple truth is that these people never truly chose us as their spouses -- they chose themselves by dragging us into their closets.  It's literally impossible for them to choose us because we aren't and can never be their type.

As for the kid situation?  It's better for kids to be from a broken home than to remain in one.  The kids will be far better off rather than being presented by dysfunction that at some point can no longer be hidden.

Good luck.  We are here for you!