L2L, I just feel like there would not have been a better way or time to tell her. Some people are disposed to being accepting, some are not. Be patient with people that aren't, because often they get behind you eventually.
With family, so many things can be running through their minds, if you put yourself in their shoes, not the least of which is that they feel they are going to lose their son/brother. Like, that person they love is going stop existing. In a lot of ways they are right about that. Not just in the sense that the person they love is not real and doesn't actually exist, but also in the sense that transition will change you on a very fundamental level, to the point that you will look back on your old self and not even recognize that person. That is one reason they resist, they are fighting for their son's life, in a way. You have to give them time to realize this is not something they can stop, and then give them time to grieve. Just remember that one of the steps in the grieving process is acceptance, and your fam will get there if they love you. Be there for them the best you can, even though it is so hard and how they deal with things HURTS you.
I know how hard it is, and I still struggle with getting my family to accept things sometimes, but it has gotten so much better.