you'll probably find its a mix of your tyres and driving style, sounds like your being to violent and and heavy with you gear change and throttle control, the key with the zed is smooth.
as for drifting with the handbrake, sounds like you watched Tokyo drift last week. you've got a v6 RWD car with a shed load of torque, and if your tyres aren't very grippy at the moment, then power oversteer should be a piece of pi$$. need to have the traction control off as well.
my recommendation, if you want to practice this technique and your private road isn't long enough. that you go and do an activities day. usually run on an airfield, costs about £40. loads of space and nothing to hit, and you can find out what your cars actually capable of. not only that but if you ask nicely the instructor will come out with you and give you some instruction as well.
usually do something like a high speed bend challenge, then onto several different sprint courses, and sometimes finish off with a giant course layout.