If your parents are concerned about the cost of using heat tape then you need to really consider how you're going to pay for heat in either the cottage or the RV. Propane for the RV will be very expensive because of the cold conditions no matter what you do to try and insulate it better. No matter how good a RV in insulated it will never be enough for freezing temperatures. Also, have you thought out a plan for dumping of the holding tanks?
I think building the 'cottage' would be much better as to keeping the place warm. You can heavily insulate it. A wood stove would be ideal heat. If you heat by electric it would be expensive. Buying an RV is going to cost you plenty and you could put that money into the cottage. Would your parents be able to utilize the cottage after you leave? If so, perhaps they could help with building it since it will be a part of their property.
Another thought - instead of a separate cottage, can an extra room just be built onto the existing house? Then it could really be utilized nicely when you leave.
...just some more things to think about. Good luck!
