Years ago, someone I knew, out of the blue, announced to her family that she and her DH were splitting up. They no longer loved each other, they were like brother and sister and the spark was gone. No one else was involved. It was just one of those things. They would continue to be friends and would work things out together for the children.
So that's what they did. A friend who was a lawyer (commercial I think, not family) did their separation agreements for them. There was plenty of money in assets and they both had eyewateringly, highly paid jobs (although friend was part time).
So, things progressed nicely etc until one day, the OW made her appearance. It was an 'accidental' phone call. She was obviously fed up of being ignored 
. Then things suddenly changed. Her STBXH came to the house whilst she was at work and stripped it of anything he considered to be his, which the DC came home to.
He chucked in his very very well paid job, so the DC had to be taken out of their private schools. They had to move areas to find schools, whilst she went full time to pay household costs but he would not sign the house over to her (which should have been done when he got the money from his) because the house prices had increased in the meantime so that would mean he had less money than she had............. and in the end she had to do it because the cost of going to court would have been more and the agreement (done by solicitor friend who did not work in this area) had not been drawn up with this sort of conflict in mind..........
He moved abroad with OW and her children, demanded his DC's attendance at short notice, even if they had to cancel a holiday.
And boy, did he accuse her of turning the children against him
At the time, it was so shocking! But what was more shocking is how many times variations on this scenario were played out amongst the people I knew as they went through their 40s (or more!) with DC who were just entering teens. (Although there was the odd one with younger children, in hindsight, only I did not realise then)
Then I found mumsnet and found out about 'the script' and it is so true!
So, OP, I would say that it is totally possible there is not an OW. But I would not compromise any decisions you make by assuming this. Make sure that you have your back covered, don't let him take advantage of your niceness, and think that you are still a team. And take good legal advice (more than once and from different sources, if necessary) and do things in a proper business-like manner. This will probably lay a better foundation for the children's future than muddling things through for the sake of being 'friends'.