I guess it depends why you're going to this other church? Are there saints' relics or a miraculous icon to venerate? Does the parish have a connection with a saint or a prominent priest/bishop? Or is it just to see the architecture?
Why do you need to tell the family if they're going to be upset? Can you simply say you're going to visit "such and such a city" for a small trip?
My family is Catholic and while they go to church every Sunday, they pick and choose what to believe (aka "cafeteria Catholic"). Mention of the stricter observances in Orthodoxy (such as fasting), which are more similar with pre-Vatican II Catholicism, seem to make them uncomfortable. It seems the stricter Orthodox practices make them "look bad" by comparison, from the comments I get from the family members, so I simply don't mention those things they will not or cannot understand.
Makes life much less stressful!