It is such a learning curve for us moms. With the 4 yo potty thing, you were super nice to get her books in the first place.
I've learned to walk away when nothing I say or do will make a difference. I try to "process" out loud. example "I am walking away because I am frustrated and don't want to yell. I am going to take some deep breaths and try again." It lets them know you are not abandoning them, but are trying to get calm. And, the steps you are going to take to calm down and try again.
We don't have pets so I'll let someone else help with that.
Hang in there! You are learning right along with your kids. It is a new skill and you can do this!