Good simple answers would be Ja det vill jag ('Yes I want to') or Nej det vill jag inte ('No, I don't want to').
I'd say "stop home" meaning I'd make a stop at home before going somewhere after. For example: "Let's stop home to change before dinner." Its pretty colloquial but common.
Stanna hemma cannot mean that. In those cases we'd say something else in Swedish, maybe I'd just translate your sentence as Vi går hem och byter om innan middagen.
If I wanted to express that, I'd say "stop off at home". To me, "stop at home" is exactly synonymous with "stay at home", i.e, to remain at home instead of going out somewhere. I don't think I've ever heard anyone say "stop home" without the preposition, but I might say "stop here" or "stop in", and with both of those I would mean to remain in the current place. I guess it must be region-dependent.