Without first reading any other answers - my reply is that I have known new relationships start after a few months (successful, ended in happy marriages), a couple of years, or, in the case of the now Mr.J2, when we met - 15 years.
In other words - there is no saying what is right and life is far too short. Mr. J2's late wife told him when she was dying that he was not meant to live on his own. She was right, but it took us a long time to meet. Your friend already knows this old flame. What the neighbours think has nothing whatsoever to do with it and can be dismissed out of hand and the kids should think about their father's happiness before they react.
My appearance was a bit of a surprise to Mr. J2's children - especially when we eloped when he was 75! All is, however, well.