Are there passenger lists for people that came to America (to visit families) and then returned to Norway? Or some way to find out when someone came and returned? I should add more to this - my great -great grandparents Ole Olson 12/19/1824-2/7/1908 and his wife Kristina Andreasdatter Sunde 11/29/1823-2/26/1914 had a picture taken in Belmond, Iowa but they all died in Rogaland, Norway. I have this picture in my collection but no date. They and my great grandparents died in Rogaland, Norway but my Grandma Christina Peterson Sunde Haugen and 4 of her family all started out in Belmond, Iowa. They all passed away here in the USA.
Generally speaking, people who arrived in the USA should be listed on incoming ship passenger manifests or airline records. This is true no matter whether they were emigrating, or just visiting. Exceptions obviously exist.
No passenger manifest exists to show a visitor's travel home. Other evidence might be suggestive of when the visitor returned to Norway. As just one example, incoming ship passenger manifests started to include more details as time went by, and one question asked was, how long do you intend to stay in the USA.