Spike, the dog who played Old Yeller, was trained by the same person who trained Lassie, Rudd Weatherwax.
There are three books in the trilogy, Old Yeller, Savage Sam and Little Arliss, but only the first two were made into films. The second book and film center on Travis, Arlis and Lisbeth getting captured by Apaches and both the kids' experiences and figuring out how to escape and the parents' search for them. The third book is about Arliss wanting to grow up and trying to ride a dangerous horse. This book states that Travis married Lisbeth and went into business raising cattle with Burn Sanderson.
Neither of Arliss and Travis's parents appeared in the sequel film, though Bud Searcy returned along with Lisbeth and the two boys, all except Lisbeth played by the same actors as in the original film.
The film was fairly faithful to the book, but a few things were changed. In the book, the pig marking goes off fine the first time, but Bud Searcy tells Travis of a small group that was missed, and Travis goes out to find them. He's not in a tree when he falls into the group, he's leaning down from the top of a small overhang to work the hogs, and the overhang gives way. Two, the burning of the cow's carcass goes off fine. A few days later, two bulls get into a fight and one must be shot, and must be burned. The body doesn't totally burn the first night, and they go out again and THAT'S when the wolf attacks. Also, Travis shoots Old Yeller immediately after the attack, rather than penning him up to wait like in the film.