The plural would regularly be Hopkinses in English. If I invited your family over, I would say the Hopkinses are coming. If I was going to your family's house, I would say I'm going to the Hopkinses' house. If you specifically were giving me a ride in your car, I'd say we're taking Don Hopkins's car.
It's not a big mystery or even particularly complicated, all regular rules of pluralization and the possessive case. I think people get tripped up in school because they see a specific affectation of dropping the S from possessive forms of the names of some historical personages, e.g. "in Jesus' name."
Seeing "Hopkins's" is very weird to me. I was taught that the possessive of a noun ending in "s" just got a trailing apostrophe. Is that no longer the norm?
Edit:
As a partially related aside, I have a friend who's right about the same age as me that's incredulous that I was taught to use "they" as a gender neutral pronoun when the subject's gender was unknown (or you desired not convey a gender) back in the late 80s and early 90s. Maybe it's just a regional difference in teaching or something. He's from the UP of Michigan, I'm from Florida. So maybe the same thing is true with possessive nouns
In practice there seems to be some variation in how people write it. Wikipedia has "List of Anthony Hopkins performances" Guardian has "Anthony Hopkins' 20 best film performances – ranked!". The s's seems rarer but the Irish Times has "Anthony Hopkins's new prestige".
In the former case it is a list of performances characterized by including Anthony Hopkins; in the middle, it is a list of performances belonging to Hopkins. The latter reads incorrectly to me as an American but as a possessive nonetheless.
It's not a big mystery or even particularly complicated, all regular rules of pluralization and the possessive case. I think people get tripped up in school because they see a specific affectation of dropping the S from possessive forms of the names of some historical personages, e.g. "in Jesus' name."