I'll second Dandylion's thoughts about spending too much time together.
Year ago I had a boyfriend who treated me poorly. We were on-again-off-again, finally I'd had enough and walked away. Lucky me, I had a job in another state and moved four hours away. I stunk at that job though, and six months later, was back in town. Hanging out with the old gang was easy - I liked old boyfriend's friends. Talking with my Mom, though, I said out loud my concern; it would be really easy to slide back into a romantic relationship with old boyfriend. I didn't want that, so I made new friends.
Your ex says he'd not ready. "...he doesn't know if he ever wants a relationship with anyone again." Believe him. Rebuff the flirting and be pleasant and cordial. It would seem as if it would be MORE confusing for the children to see you guys flirting and huggy one day, then not at the next occasion - and you say this is happening. Frankly, I thing two years is nothing in the grand scheme of things, but I've been wrong before.