Well, I'm not a parent (though I'm definitely old enough), but I wouldn't necessarily want my kid to do something without asking. That being said, if the rational arguments of explaining what you'd like to do, showing them this website (or another similiar site) in order to let them know you're researching how to do what you want to your hair safely, and just generally kissing butt don't work, you might be able to invest in some clips/falls/etc. These change the "color" of your hair without dyes. There are some absolutely gorgeous clip in pieces available. Frankly, I may be facing this option in the near future myself!
These hairpieces are widely available online and if you've got a local "rock lifestyle" store (like Hot Topic or something similiar). Good luck!!!