I'm sorry that you're going through this. I understand 26 years is a long time to be with someone.
I have never experienced a relationship that long, as I am only young myself, but as a child of parental separation I can vouch that my parents are happier now than they were when they were together for 20 years. So, I would say, no don't beg for forgiveness. You deserve to be treated better than that. The marriage will only go back to the way it was, and do you really want that?
I assume you've heard the phrase "this too shall pass"? It's something I repeat to myself when I am experiencing sad thoughts or distressing life events, such as a break-up. It will pass. Feelings of sadness and loneliness are normal after a break-up. Especially after a relationship of 26 years. But they will pass. Allow yourself time to grieve, but remember to pick yourself after and remind yourself of who you are and what you deserve in life - and that is everything.
As Betternow suggested, my advice would be to get in contact with a GP and maybe get a referral to speak to a psychologist or therapist to work through these hard emotions. And yes, family breakdown is common, I have been through it. But I can proudly say my family is happier now because of it, and my parents have found new partners who treat them well - all I want is to see them happy and I am sure your children will want the same for you.