I like very much your home definition. We have almost the same approach.
For me, home is where you feel loved and supported and where you are you and only you, without worrying about the opinion or thinking of others.
In this case my home could be anywhere, if I love myself first, if I remain free, and happy as I am. Today I don't have a partner, I have decided a long time ago that I will wait for the right person with whom I can really feel that. But every day I find myself more and more demanding. So I don't know.
On the other hand, when I'm around my family I also feel at home, even though we are all so diverse in ways of thinking about oneself and about life in general.
Having the right partner can give one a sense and feeling of being home no matter where one might be...the togetherness, the bond, respect, passion and so on...all those things speak of home to me in respect of my partner; I think you'll agree. And yes, family can bring similar feelings.