It's too bad, Todd, that you didn't have the opportunity to see A Dog's Purpose before seeing A Dog's Journey.
Seeing a film's sequel first isn't usually the best way to fly. I read the books first and was so engaged in the original book that I was absolutely thrilled to find that the author had written a sequel and the original story was continued.
In no way can I guarantee that your opinion on the film and its themes would be any different if you had seen the original film first, but maybe.
Your premise that the movie wants the viewers to believe that dogs can be reincarnated if given a specific task isn't really true. The films/books do tell the story that dogs (such as Bailey) are reincarnated and come back as other dogs--but it's not really predicated on anything done by a human.
I believe we are supposed to think that Bailey is in a unique situation in that Ethan has caught on that the dogs in his periphery all seem to have a common knowledge of the original Bailey's experiences.
In these two films, Bailey is trying to suss out his "purpose" in life (in a rather philosophical way) and after believing that he discovered it, continued to get a better understanding of what his actual purpose was after living more lives and being able to remain intertwined with the same human characters.
And I'm a little surprised you'd not be thinking that a dog movie is going to be a tear-jerker. It's hard for me to think of one that isn't. A Dog's Purpose/Journey, The Art of Racing in the Rain (in which the dog fancies he might be reincarnated as a human--after he watched a documentary on TV about Mongolia!), Hachi: A Dog's Tale, The Adventures of Greyfriars Bobby, The Incredible Journey/Homeward Bound, Old Yeller, etc.
I haven't cracked open my copy of Dog's Journey yet, but am thrilled you are so keen on the treatment it was given by Universal.