>>4 I agree with Yasaine. The best solution would be to try to get your parents to understand what meditation is about. If it's something that really helps with your depression and anxiety, and if you try to explain it to them from that angle, maybe you could get to a point with them where, even if they may not like it, they understand it enough and can see what it's done to benefit you that they wouldn't react negatively towards you for practicing it, and you wouldn't have to be afraid of being "caught" meditating.
If you can't reach a middle ground with your parents, and if there's a time of day when you're home and they aren't, you could use that as your meditation time. Also, you could try turning your back to the door when you meditate, using the physical act of having your back to the door as a mental trigger to shut out your awareness of it and what lies beyond it (the rest of your house, your parents, etc.). That may help with focusing.
As for a different way to meditate, if what you're doing works for you (and it seems like it does, from what you've said), I don't think you should worry about finding a different way to meditate.