Not really; you can't learn technique against an opponent at home especially by yourself and you need direction.. A better idea would be to enroll in a Brazilian Jiu Jitsu Course, as MMA is highly based in BJJ. Your parents should be more inclined to pay for this as it is a pure martial arts form
really there is no way, unless you are already a submission and boxing expert you absolutely need to have instructors and sparring partners, and no DVD's will not show you what you need. You can how ever start getting ready for MMA by getting your conditioning up and getting jacked. Get a good cardio program you will need to be able to run about 3 miles and then practicing your boxing and wrestling for at least an hour. If you show your parents that your committed they might change there mind.