If by re-arranging the word order you can put an "of" in to replace the
apostrophe then you should use the possessive. So another way of saying
it is
This is a gift from the family of Jordan, though in this one you would probably put in the Firstname too.
The only time you don't put in an apostrophe is when you use pronouns. So his, hers and its DO NOT have apostrophes.