It seems callus, but you do have to consider for how long will it be used 24/7? The caravan and boat stuff is not as economical as normal house gear, but it is small, and in some cases cheaper. My caravan always has electric huck-up, but still water and central heating, both carver are gas powered from a gas cylinder. There are also oil powered units which we used in the narrow boat. The Eberspacher heater we had on the boat heated water, and through a Calorifier (heat exchanger) it did the engine, domestic washing and domestic heating, and are very small, and compact. However because they are not as efficient as normal domestic equipment they are in theroy not permitted, simply because of the efficiency, and building regulation rules. Also wood burning fires in many houses, in theroy, are not permitted as you are only allowed a drop of efficiency of 5% so any house heated by any other form of heating in the past can't in theory use a wood burner, but of course they do.
Some of the latter caravans have the option of either gas or electric, and one has to consider the caravan only has a 16A supply. Caravans do have showers, but since you get water in a barrel from local stand pipe clearly designed not to use much water, we would always try to use showers provided by the site.
In essence the granny flat is very like a caravan in that the occupant can come to the main house to do some functions. And since better insulated than a caravan it should in theroy use less power than a caravan to maintain. One would hope correctly designed a small electric panel heater should be enough. In my mothers house we had a problem with temperature so have independent thermostats and timers for bed room and living room, using that method in theroy you should not need both rooms heating at the same time, so in theroy 1 kW is likely enough for heating. If that is the case then simple panel heaters would do the job, but powered from a thermostat and timer. For a 20 year time then having gas piped in and full central heating is likely the best, but for 5 years then likely simple panel radiators.
I have same problem, my mother at 91 is at the moment living in he own house on her own with carers 3 times a day, to convert garage to a granny flat possibly it will only be used for a short time, however she could live to 100 or more. However health wise even if she did likely she would need special care I could not provide so unlikely to use the flat for more than 5 years. Can't use house because she is in a wheel chair, and house not suitable for wheel chair use. So in real terms if her condition deteriorates only option is to go and live with her. However father-in-law is 89 and lives next door but one and he also needs care, so I would not be able to live with my wife we would have to live in separate houses. It is never easy. Once one dies then easy, but both in good health, but alzheimers is kicking in with both. At least my father-in-law has two other children, but life is never easy!