With the Pomegranate, or Rosemary, what is considered cool inside? And what temperatures can they take outside?
Outside; both can tolerate fairly low temperatures but I do not allow them to freeze. When it gets too cold outside I bring them into an unheated garage. As winter progresses and it approaches freezing in the garage, they are shifted to a cool basement. They could stay there all winter under fluorescents or eventually moved to a brighter, warmer location to begin growing. By this time it is well past the new year.
As far as actual temperatures inside; different sources give different numbers but probably the cooler the better especially for the Pomegranate which will shed it's leaves and go truly dormant. Pomegranate can stay dormant all winter if you have the right location.
Rosemary will not go fully dormant but a rest period certainly would not hurt. Again, I don't think you can get it too cold in your home. Rather keep them as cool as you can manage. A greenhouse would really be a big help with these types of plants.
I am looking for a tree that I can groom and give to my next generation if need be, and not really worry about them killing it by accident, at least if they take care of it.
I want a tree that can be taken care of in doors during the winter, and outdoors during the summer, or in a greenhouse setting if possible, since when I move next that is probably where I am going to be putting most of my plants.
Again, Ficus is a good choice but will not tolerate freezing. Between the summer and the cooler months in the greenhouse it could stay under natural light most of the year only being moved inside for the coldest months.
Overall though, I am very partial to Chinese Elm. They can be grown outside in summer and, provided you allow a rest period
, be brought inside under appropriate lighting. This plant would also be happy in the greenhouse over the winter, as would the previously mentioned Pomegranate and Rosemary. With the Rosemary you get the added benefit of the occasional pruning to be used for cooking.
Most any of the traditional bonsai material can be kept as you describe, outside in summer and in a cold greenhouse over the winter. Although deciduous material will, of course, lose their leaves.