I'm so sorry. This phase is tough, but it does get better. The others are right. Don't engage with him, let reality hit him in the face. It's one thing having the excitement of an affair along side the comfort of home, but quite another when it causes you to lose everything.
As for telling people, don't worry about his opinion on this. Of course he won't want people to know, as once they do he'll have lost their respect forever. Think of you. Right now you need real life support from your friends and family, so tell them. I was amazed at the response I had, everyone was there for me. No one judged me, or made me feel embarrassed, they were just incredibly kind. His family need to know too, but it is quite likely they will close ranks on you so be prepared for that. My MIL is lovely, really lovely, but I was left in no doubt that when the chips were down her son came first.
As for how I told people, I rang my parents (in tears), I told my best friend when I saw her, I told my SIL by email, I basically let people know in a way I was comfortable with. I relied on them to let other friends and family know.
This is only the start of a long road. You may split, you may stay together, decisions like that are for you and you only. No one can tell you what is right, as all relationships are different. Beware hysterical bonding. It's very common, you talk, cry, bond and have amazing sex with your DH. It doesn't mean everything is solved, or your marriage will definitely survive. It might, but this kind of full on emotion isn't real or lasting.
I promise you you'll get through this and come out stronger and happier. You won't believe me now, but in a year from now you will.
Right now look after yourself and your dcs, and get legal advice.