If I appear in a magazine cover, and get $2,850 for doing so, do I have the right to split the money (50/50) with my cousin?

Why would you want to split a measly amount with your cousin? Does she or him have a secret about you and will spill it out, if you don't share half the money with her or him?

If it's only your money, than no.

$2,850 is not very much do to a magazine cover. If you're that good try a better magazine. You didn't say what your cousin has to do with this. Be more specific.

If you were lucky to get a chance to come to magazine cover photo then the money is yours but if you have got the ads because of your cousin then you have to split the money.

If it's only your money, than no.

Well, it depends really. Because if you're legally an adult, any money you receive can be dispersed however you see fit. But if you're a minor, your parent or legal guardian will hold the money in trust until you reach adulthood, and this may take the form of a college fund or other trust that cant be broken up, except under certain conditions. 

Your money, your call.