My family supports me whole hardheartedly, although my dad could care less what I do, just as long as I get a job to pay off my loans. I think it's mostly because he has almost no idea what I do... I think he just thinks I make pretty pictures all day. I once told him I couldn't come home one weekend because I had a ton of homework to do still, his was response was "Well can't you just draw faster? That's what you do all day, isn't?". Parents just want their kids to be successful, and most of the time, for parents, success = being a doctor, lawyer, accountant, ect. There's that stereotype of the 'starving artist' that people always think of, and the only ones who are 'rich' are the ones who are dead. Of course this isn't 100% true now, and there are plenty of successful artists in the industry, most people just don't know about them. Heh, for example, not too long ago, when Glen Kene left Disney, I was trying to explain to my dad just how important he was to me, and what he worked on at Disney, ect. He didn't really care, and I could tell he was spacing out even when I told him which Disney Princesses he designed and such. He just doesn't share the same enthusiasm for it as I do.
My advice for you... Just don't worry about it. If you really like art, then do it. Of course I don't know your exact situation, but make sure you do art even if she doesn't really approve it. Maybe giving her a drawing you did as a gift or something could help...I dunno, I'm just talking now.