Ok Gerry, here goes....I call a stick a stick I am afraid! I would tell the kids in your way, but in my opinion they need to know about the illness, no matter how hard it would be. You say you are worried about them being bullied about it at school, but unless they choose to tell anyone why would anyone know? I just worry that if you don't tell them and it all comes out later (months, years, whenever) that they could end up being resentful that you were not honest about it - they then have the opportunity to ask questions if they want to and at the end of the day as a fantastic mum you will be there for them anyway.
Regarding your op, keep talking to them and try to make them understand all of the reasons why this is so important to you. It is only natural that they will be worried, but at the end of the day although you are doing this for your kids, you are also doing it for you - to give yourself a chance of a better future.
Sorry you are having such a hard time of things and sorry to be brutally honest regarding my opinion - but you asked!! Things will work out whatever you decide, one way or another.
Good luck with a tricky decision xx