By "pictures of my family", I'm assuming you mean indoor candids at parties, etc. If that's the case, it's possible that you may be able to get by with a high-end compact like the Panasonic LX7 or one of the other cameras that Gordon compares it to in his review
On the other hand, since you have people you can swap gear with, that's a good point for moving up to a DSLR. The only thing I would add is that you may want to look into buying a fast/bright (f1.8-ish) 35mm or 50mm lens. (Unless someone in your circle already has one that you can use.) But since both Nikon and Canon have affordable lenses that meet that description, that doesn't really help narrow things down.
On the plus side, it also means either camera should serve you well - Mark