I haven't had many problems with Cats and Dogs myself.
I start by getting the friendship up with the dogs. Leashing them, taking them outside to a grassy space, unleashing them and giving the poop command started them going outside, worked on that front. I found Loyalty, adventurous and hunter made them eager to learn, follow and interested in the flora and fauna). Mine sniff around when I send them out hunting and always bring home something. (I follow them around with the right click and it's a good way a checking out the neighbourhood. The Sims dogs work best as a pet for one Sim and more and more commands pop up as you go further. Cats do their own thing and I don't play them as much. I am not a cat person!
I had a little rescue dog myself in real life and it took a long time to go from unhappy stray to a loyal and loving dog so I use the same patience on the Sims ones.