Just to play devil's advocate- something very very similar happened to me many years ago, and I eventually, after much soul searching chose to stay with my dh.
I know that many people think I made the wrong decision and may think I'm stupid but I'm now at peace and happy with the decision I made.
In the first few weeks I felt very much as you feel now- I was intent on separation, very practically minded. Dh moved out. I too have dc and worried deeply about the effects a separation would have on them.
I grieved the husband I thought I had. It's very hard to describe the pain- it's like they have died almost and you are stuck with this man that you know nothing about. You also grieve for the life you had- the house, the lifestyle etc. and I think it's very easy for others to say they will walk away from everything when it isn't their reality.
Very much like your Dh, my Dh was devastated and did not want a separation. He was also in other ways a good husband and life partner (although in this instance/situation he was far from a good husband!)
In the end, after much soul searching, I decided that if he would be committed to attending sex addiction therapy and also couples therapy that we MIGHT be able to make it work. I also attended therapy on my own to help me sort through my own feelings.
Therapy was incredibly useful in helping us both understand why he did what he did. The reasons were very complex and had deep roots into his childhood.
It also allowed me to talk through my feelings and made me realise what was more important to me...stability and familiarity and the person I had been with for 30+ years.
I want to make it clear, it was not an easy decision or an easy path to tread. In some ways it would have been easier to separate.
Has it been hard work. Yes. Have I cried a lot. Yes. Do I still love him. Yes. Would I 100% trust him again...No- but it has made me wiser and in many ways has improved our marriage. Our communication is better, we don't take each other or our family unit for granted.
He understands that if he ever let's me down again, there are no more chances.
I accept that everyone reacts and feels differently about such a catastrophic breach of trust within a marriage, but I don't think you know how you will react until it happens, no matter how much you empathise with a situation.
If you have made your mind up then please totally disregard my post, but I just wanted to give you perspective of an alternative.
Please look after yourself, don't bother what anyone else thinks- only your opinion matters now xxx