If you take part in an activity that is legal where you do it, but illegal in your home area, should your home government be able to punish you? For example, using recreational marijuana
You mean like Utah? In Utah you are charged with possession of a controlled substance if you have any trace of it in your blood. Period. Vacation in a"legal" state and then return to Utah, get busted and tested and it's off to prison.
No. I believe state laws should be like embassy laws. When I visited the Swedish embassy for an event back in 2010 I was able to drink alcohol despite being 19 at the time.