I read a book when I was around 10 that was a serialisation. I only read the first book and it ended with a dog being separated from its family while on holiday. I haven’t stopped thinking about whether the dog ever found its way back home ever since. The dog’s owner was a young boy, I can’t remember anything else unfortunately.
Lost Classics of Teen Lit: Name That Book! 
Sounds like either Ribsy by Beverly Cleary or That Dog Tarr by Nan Hayden Agle. Both dogs were owned by boys. Ribsy was the mixed-breed dog of Henry Huggins; Ribsy leaped out of the car without his collar (including tags) on after Henry took it off so that Ribsy could scratch at a flea. Ribsy met all kinds of people on his way back to Henry including a family whose car he got into by mistake and a sweet little old lady who cared for him like he was a baby.
In That Dog Tarr, Tarr was a lab who had this loving family (including a boy whose name I forgot… but the boy gives him the nickname of Cerberus). Tarr wound up getting dognapped and sold to a family with a dad who was told he was a hunting dog. Tarr was gun-shy and ran away at the sound of the first shot, got picked up by animal control and was found by his owner just before he could be re-adopted by the family with the dad who was a hunter.
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