You can always write about the Williams family or the Watkins family, but the rule in pluralizing a name ending in S is, as you would expect, to add —ES. Therefore, the first family in the previous sentence is the Williamses and the second is the Watkinses. I can hear you shouting about how weird those names look. What I find interesting is that people have no problem saying or writing “keeping up with the Joneses.” Why then is it difficult to want to keep up with the Hopkinses or the Chamberses?
That Jones family has been around so long that we are all inured to the plural. Chances are even if you write the plural correctly for other names, you will still pronounce the plural form as the singular: you’ll drop the sound of the —ES: “We’re having dinner next Saturday with the Hopkins
(ES).” But do write it correctly.
Adding an apostrophe does NOT make a plural: “Watkins’s” is the possessive form of one person named Watkins, as in “Dr. Watkins’s umbrella.” In fact, you can drop that final S after the apostrophe and you’ll still be correct. However, writing that you are “having dinner with the Watkins’s” is always going to be wrong.