I think they're being unreasonable.
That said, they do have the right to decide they don't want a relationship with you.
I'd suggest maybe sending one note, simply saying that you are open to discussing this if they would like, and the door is always open. This note should not include any statements about missing your GC, how awful it is, how much you've done for them, etc. The goal is to keep it as neutral as possible so they understand you're open to reconciliation, but they don't see this as emotional blackmail.
After that, if you get no response, I'd suggest just waiting. If you try to see them or the children, you could well drive them further away.