If that was your house, would you water the grass? Is it the right thing to do? Reminding yourself of your 2 kids won't help the grass, or property value that you'd share if it doesn't work out in the end.
I know what it is like waiting for my spouse to turn to me and say that she'd love me unconditionally. She didn't. She had some conditions that she said, many that she didn't. I still have to look up at the mirror and see me, though, don't I. I have to feel good with that person.
I have 5 kids, 4-11. I know kids can get in the way. They can also have fun helping.
BTW. If he kissed you on your forehead, why didn't you kiss him back on his? If you think of the emotional needs he never had met (and you about yours), you may see some gaps you want to fill for any relationship. Being a great catch doesn't mean you are a great catch for him. We change over time. He or you may have changed and are no longer a great fit.
I would do a lot to be able to stay with the mother of my kids. She wouldn't, though. For her, it was all about me. I was the screw up in her life. So that's a fit I can't fix. But, if he comes by and sits on the bed, there's something in that house he wants(ed) back. It is much easier to say, "your child is awesome" than to use specific adjectives. It is even harder to use evidence. What makes you a great mother for that man? What makes you a great catch for that man?
Either way, it has been a long time since he moved out, so thinking about him might be nuts, anyhow. If you are, though, embrace your hope with evidence-based actions. Water the grass.