Ernest you just need to do whatever feels OK for you right now. You will probably find that changes from one minute to the next, but don't worry about that, it is completely normal. I found one thing that really helped me was to always be in the right, and behave as well as I could, so I always felt I had the moral high ground. Of course this also completely wrong footed my ex, so maybe not the best when I was trying my hardest to make things work again, but it does mean that looking back I feel that I did my best, and that when I one day talk to the children about it I will feel no shame about any of my actions. I also think that it helped me feel at peace with myself (whilst raging at him, fate etc).
The other thing to bear in mind is that for your dh his affair was probably a complete fantasy. I say this because what you are describing is very familiar, and other mums here who have survived affairs have said that's how it was for their dhs. That doesn't make it any less hurtful, but all that "love of my life stuff" seems to turn out to be incredibly shallow, almost a play act, with no foundations. My ex wrote the most incredibly gushy e-mails to his mistress (that's how I caught him), totally out of character, and incredibly hurtful because he never ever said anything like that to me in the 15 years we were together.
I very deliberately did not boot out my ex (although that's always what I thought I would do, along with cutting up all his clothes etc etc) because I wanted him to have to make a conscious choice to end our marriage - he didn't get to make any decisions about ending his affair because his mistress dumped him the second she found out I knew. So he didn't leave until about 18mths later. It was very hard at times, and the children did pick up on tensions, but they were fairly little (I think 3 and 4) and I don't think it was too awful for them.
Finally don't expect your dh to understand how you feel or acknowledge what he has done to you for a long time. You may well find he wants to brush the whole thing under the carpet as quick as possible. I would really try and get him to sign up for counseling, and get some support yourself too. If he is really keen on staying and talking then that may not be a bad thing, but make sure it is on your terms.
Please do not feel bad about yourself, or compare yourself to the OW. Your dh has just made some really bad decisions, that he probably regrets, but the reasons were his own, they are no reflection on you. So he has been unhappy for a while, well it was his responsibility to do something about that, and he chose rather than working on what he has, to branch out into fantasy land. He found a willing accomplice, who was probably in a similar position. I don't suppose either of them had any intention or thought beyond the immediate as clearly neither of them were free, so I really think this was just escapism.
Hold on, and spend as much time just enjoying your little ones, and the other things about where you live and how you live that you enjoy. find out your rights and get yourself as empowered as you can be, and then start to think about you really want to do. But don't be surprised if that takes months rather than weeks.