Why is it that addressing holiday cards is such a controversial topic?
This is not a matter of grammar, but of style. It's your name and your card, and you don't need to follow anyone else's rules if you don't care to. Besides, matters of family tradition, and of pleasing in-laws, are not resolved with citations from the Internet.
In current English usage, apostrophes signify possessives, not pluralization. Usually, the plural of a name ending is s or z is signified by adding -es. The AP Stylebook, for example, asserts
PROPER NAMES: Most ending in es or z add es: Charleses, Joneses, Gonzalezes.
Similarly, the Chicago Manual of Style states flatly
Names of persons and other proper nons form the plural in the usual way, by adding s or es:
… flouting the Joneses
Note that the apostrophe is never used to denote the plural of a personal name: "The Schumachers left for London on Friday" (not "The Schumacher's …")
Such examples assume, however, that you would pronounce the plural of Jones as Joneses, adding a syllable. Whether you write Dickens' novels or Dickens's novels, or an herb garden or a herb garden, depends on how it sounds in your head. In the same vein, I would say if you pronounce the plural of Barnes indistinguishably from singular Barnes, you have liberty to sign the card as love from the Barnes, nitpickers be damned. Alternatively, you can sidestep the issue and offer love from the Barnes family.