Most of the older Christmas songs have only a few chords. Away in the Manger, Silent Night, All Through the Night, that sort of thing. Jingle Bells is pretty simple too (although it's not quite as old as the others, I don't think... and it's technically not even about Christmas.)
On the other hand, many of the songs written in the 1900's tend to be a lot more harmonically complex. They were written during a time when "harmonically complex" was simply the way songs were made. Winter Wonderland, Have Yourself a Merry Little Christmas, The Christmas Song (Chestnuts roasting...), and so on. Lots of great, jazzy changes. Not so easy to teach!
Not that simple, modern Christmas songs don't exist. Grandma Got Ran Over By a Reindeer, The Chipmunk Song, Feliz Navidad, etc.
Anyhoo... Jumpin' Jim Beloff does indeed have a couple of books of Christmas songs. Not too expensive. But my favorite book is Hal Leonard's "The Ultimate Christmas Fake Book". It has tons of Christmas tunes, with lyrics, melody (standard notation), and chord names. It does not tell you how to play the chords (no chord diagrams), so you might need to keep a chord chart handy. You'll definitely find some good ones to teach your family.
JJ