I think this is a situation where you will save time, money and aggro if you go directly to your solicitor, or whoever holds your land deeds, to find out what the law states in
your particular position. I imagine your parents would have had 'grandfather rights' to park where they did, but I don't think those are heritable. With more cars on the go, the neighbour/landowner could have been ok with one car parked there, but not several. In all probability you will end up as Anke says, turning a piece of your own land into parking spaces. An unsatisfactory alternative could be to park by the road, unless you have a long driveway. You don't mention if the track to your house is tarmac or dirt, or who it belongs to. Do you have only a right of access to get to your house?
By finding out the legal position specific to you, you will avoid an unpleasant situation where you feel bullied and your neighbour feels hard done by: whatever the law says, then both of you have to comply, and it becomes less personal. Fights over land boundaries , rights and access date back into the mists of time