This is the question everyone hates to hear, but how old are you? Your age (both actual and apparent) can affect how you're perceived in anything you do, especially with a fringe skill like magic. When I was 19 and trying to emulate David Blaine, nobody took me seriously. Now that I'm almost 27 and I go around acting like an escaped lunatic, people seem way more into what I'm doing. I don't quite understand it.
Also, what do you mean by "take you seriously?" Are you finding that people don't take your career aspirations seriously, or do you feel your spectators' demeanor/reactions aren't serious or intense enough?
On a general basis I try to make my act as much fun as possible, so to do that I make sure it's fun for me to do. If you're not having fun, your audience won't be either, and that's important to remember even for an act with a serious tone.
If people aren't taking you and your magic seriously, that might just be a matter of time spent with the craft. I'm not a serious act at all, but people can tell that I'm dedicated and skilled at what I do partially because of the amount of costuming and props I've lined up and partially because of the depth and strength of my character performance. People can tell almost at a glance that I've spent a great deal of time, money, and energy fashioning myself into a pink wizard and gaining the skills and story that go into my act. It might be that once you've spent more time building your magic and your character and shown a great level of dedication to it, people will be willing to take it more seriously.
Also, if your family isn't taking you seriously, ignore them. That's totally normal for families to do. If your magic career really starts to go somewhere, I'm sure they'll be more supportive, but early on it's probably going to seem like a lame hobby to them. They know you, so they're less inclined to believe your character. In that way, performing for strangers is actually better.