I had a photo posted earlier that turned out to be incorrect in terms of where the theater was. I have since found an actual photo of the place on the Facebook page for Mancelona history. I also found obituaries for some folks who were connected with the theater. One from 1957 was for Emma Mae Guthrie who was the former operator. Another was from 2015 for Harold Wilfong whose family owned the place in the late 50's and early 60's.
The Family Theater name comes in the 70's when it was mentioned they lowered prices. The theater showed the Steve McQueen classic "Bullitt" in 1969 as the Lona but a 1976 article has the "Family" name. King Chuck indicates the BP station is where the theater was. After analyzing the photos I found he is right. Several buildings in the downtown stretch have been demolished. I will use the BP address for reference (see comparison photo analysis below).
2 commenters indicated the theater building burned after a distraught high school student rammed into the building during a police chase, causing a fire. I searched for news articles on that and found nothing however.
I also don't know if the Owego in Mancelona is the same theater either. The only mention of an Owego theater I have found is in Deckerville. I saw no reference of the Owego in any of the historical materials I found for the town. That doesn't rule it out because lots of historical information omits mentions of theaters for some reason.