There is no right or wrong way to deal w/someone in crisis. If you discover something that is working, then continue to do so. When something isn't working, chuck it.
I am glad to see that after your messages, he began to reach out to the children. Maybe he thought everyone was angry w/him, but you opened the door and allowed him to step over the threshold and enter into a "safe" place to communicate w/them.
Sometimes, we have to take a chance to see if they will nibble the crumbs that we offer. I think you did the right thing by reaching out as a "friend". If he knows/senses that you aren't expecting things of him, he just may reach out more and more as time moves along.
I'm very proud of you for taking this step...hopefully it will continue to pay off for your children and their father will want to spend more time w/them.
Sit quietly, the answers will reveal themselves when you least expect them to. The past is gone, the present is a gift and you need to focus on today, allow the future to reveal itself when it is ready.