I found that a good way to get trainer points is by feeding your dogs when hungry, giving them water when thirsty, winning competitions with them, petting them, giving them treats after they do a trick you asked them to do (I think this also helps them to not be confused by commands), giving them baths, brushing them, and taking them for walks. Dogs can each raise their happiness 200 points per day (you can view their happiness by going into the dog's info and clicking on their picture). As far as how much a cat's happiness can go up in a day, I don't know. I haven't had the patience to get it that high because they are pretty darn hard to please.
Oh, and in referrence to the person who wanted to know about how to boost your dogs' physique? This is just a guess, but try giving it some Diet Food. It appears in the normal Barc store (not any of them you encounter on a walk) after you get a certain amount of owner points.
I've been trying to discover a lot of secrets about this game and I think I've become relatively versed.... If you guys have any more questions, please feel free to email them to me at email@example.com
and I will try my best to answer them! ^^
Hope this helped~!