Brummie,
Here's how we did it. We were together for 11 years, 4 dating, 7 married. It was similar in that no third parties were involved, no anger and fighting. It was just over.
For about six months, we saw each other / talked almost every day. After all, he was my first, and I his. We were both a little lost.
Then, we had a talk and decided that it was time to cut the strings. Now, we had no kids, that is true. So we did not have that tie. Anyhow, after the six-month period, we no longer socialized, or talked on the phone. From then on in, our contact was limited to talk of selling our home, the divorce, and once every few months phone calls to touch base. After the divorce, we just said "adios".
We are not friends, we do not hang out or anything, BUT, I would still trust him, I still care deeply for him (not in 'that' way, but as a lovely, beautiful person), and no one had better ever say ANYTHING bad about my ex. There is a reason we got together, it's important to remember the love that WAS. Sometimes things don't work. It's not a blame game, it's just to be accepted.
There will be stressful times, but I sincerely hope that you can remain 'friendly', and work together as a parenting unit.
The lonliness of just 'being alone' was hard at first. But, after a while, I learned to deal with it. Missing the children, and the little daily routines, will be the hardest. I will be thinking of you, and please know that it will be okay, in time.
And remember, it's not weak to cry. Really.