I'm a pretty strong willed person (shocker, no?), but family is a tricky thing. I'd certainly take a few moments to figure out what caused the initial rejection of my dream -- concern for my well being, a selfish desire to mold me into what they find appropriate, etc. -- and go from there. Also, there are a few relatives I can think of whose disapproval may very well be the biggest push to get me to follow that dream. Ultimately, there is very little in life that is as important as following your dreams and doing everything you can to live the life you want, but at the same time, I've been isolated from my family before and it ain't fun. Also, I've been in situations in which I would have benefitted from listening to that unwanted familial advice.
This is a tough one, so I'm going to sheepishly back away and give it to the next person.