Learn English – also call the brother the relative

As noted by commenters, this may depend on the culture; but my own opinion is that it can cover even fairly distant relations, provided that the family relationship is the reason for the continuity. So, if operation is transferred from father to son-in-law, and then to son-in-law's younger brother, then to that younger brother's granddaughter, and then to that granddaughter's cousin, and so on, then it's still been "run by the same family", even though at this point the original manager and the current manager are essentially unrelated. On the other hand, if the enterprise is put up for auction, and the second cousin of the current owner-and-operator happens to place the winning bid, I'm not so sure that I would count that. (But "the same family" is sufficiently vague that the new owner could probably get away with making the claim.)

To take a step back in time would literally imply traveling to the past. However, this phrase is nearly invariably used figuratively: "It felt like taking a step back in time." This implies that some aspect of the situation was similar to something that would have been common in the past.