My advice is to change how you express what you want to say, so you're telling her how you feel, and asking questions about how she feels. So the things you want to say would translate like this.

You sound like my dad becomes My dad did/was ___ and I can't help thinking of him when you do/are ___, which makes me feel ___.

Stop yelling at them becomes It makes me feel ___ when you raise your voice to the animals. I wish I knew how to stop this from happening.

You need to learn not to be so angry becomes I feel like the animals make you angry and that makes me sad for you and for them. What's going through your mind when that happens? What can I do to help? It upsets me to see you feeling so frustrated.

It also helps to suggest something to do, rather than something not to do. So for example you might say: Look how X animal responds when I do Y! Isn't that cute. That might come in handy when you're trying to do Z. If you yell at him/her, he just does X.

I also wonder if you maybe just need to split the jobs up differently. Okay, she doesn't want the workload for the cats. Can she do something else instead? I hate taking the trash out and my husband hates cleaning the toilet so we don't ever split those jobs between us, for example.