I think if the child wanted to go on and see how far they could achieve at that elite level, then I would be all for supporting them. However, I don't think I would split the family. Either we would find a way that we could all go, or find the next best alternative where we are, until the child was a certain age that I wouldn't mind them going on their own, say at 16. Also, I don't think until children get to say their mid teens that sport should be taken so seriously. Its fun and should be fun for them to do, so that they love doing sport and will take it into their adult lives.
My dh is a hockey player and our weekends often revolve around that - we'll let the kids try hockey but if they don't want to play hockey and rather do another sport than thats fine, we'll encourage them elsewhere. the only thing my dh won't let them do is play for a diff hockey team! lol

I think the reason that alot of athletes compete in the same sport their parents did is often just due to the fact that they are exposed to that sport from such an early age. My dd isn't able to grasp things in her hands yet, but dh is intent on her getting her first hockey stick by the time she's one! I coached under 9 hockey for a year and coached the daughter of a bloke who played with my dh, and his wife also palyed - she was 6 at the time, she is now 9 and has been selected for the u13 state side. I don't think its being driven by the parents, its just that is always been a thing in her life and so i suppose maybe natural that she would want to take it up, which i'm guessing is the same with many big sporting families.