In "lightweight" TT you can tow with an F-150 likely won't be very suitable for a family living in it full time.
My family of 4 gets along quite well with the 6 cu ft refrigerator in our TC. On a 2 week trip we usually have to go to the grocery store once a week but we have to do that at home anyway.
If you're going to be plugged in all the time I wouldn't worry about solar. Wind is a complete joke for an RV. An RV will generally use a LOT more electricity than a house of the same or even much larger size. RVs are very poorly insulated. A typical RV absorption refrigerator running on electric uses about 3 times more than a standard electric refrigerator in my experience.