I would go with a "cottage". The 12x24 size is readily available at most shed dealers. It can be moved and placed where you want it in the yard. Insulate it well, and it will easily hold room temperature with a small, efficient space heater. You could hardwire it into the house fairly easily, or just run a few extension cords...
Like another poster said, you can use a portable toilet.
Since you have access to the kitchen in the house, you shouldn't need any electrical appliances in the cottage that draw a lot of power. Maybe a small dorm fridge and small microwave???
In 5-6 years, when you are done with the shed, you can sell it, and recoup most of your costs. You can't always do that with an RV, as they depreciate very fast.
I have a 8x10 chicken coop that is partially insulated, and an 11x11 tack room that is floor to ceiling insulated. Both are heated in the winter - coop with a heat lamp, and tack room with an oil-filled heater. Both stay toasty warm. Spoiled chickens and barn cats, I know...
