What the readers say
Take yourself back to your school days. Now imagine that your parents were separated, and one of them started going out with one of your teachers. No matter what your school age, you're bound to be mortified at the thought of it, and what your classmates are going to say. If your son is pally with his coach then he's no doubt a good player, so don't risk messing up his place in the team by indulging in this fantasy of going out with a younger man.
You say your daughter has a bit of a crush on him, and I think it's the same for you too. In both cases, it will pass -- attention from a young, attractive man is flattering, but it's not worth embarrassing your kids for and making life difficult for them at school or rugby practice.
You clearly think the world of your kids, otherwise you wouldn't be so concerned about their possible reactions to this situation. You are even worried about your daughter's little crush. You've also committed yourself to the challenge of raising your kids single-handedly since a very young age.
Well, you should be proud of yourself, and, having stuck it out without entertaining the idea of having a boyfriend for so long, I think you deserve to have this handsome young man come your way. If you're sure that he's interested, then I say follow your heart. Your children will understand and would probably even be delighted about your new enjoyment of life.