I read your plea and it reminds me very much of my experience with my three children and my ex. He was very different from me ,especially as I matured and he didn't (which led to our eventual divorce). We did not hold the same values and I was constantly concerned that my children's contact with their father would effect their how they view the world around them and interact with it. Unfortunately, a lot of our differences were cultural and sociological and not necessarily "detrimental" in a sense that a court was willing to find such.
Seems to me that you may be in the same situation, or also be over reacting to a young child's typical behavior. Here's some suggestions:
1. If you feel that your daughter is acting out due to her father teaching her violence, then I'd suggest speaking with a child pychologist/professional to see about modifying your child's visitation schedule, or possibly asking the father to participate in some counseling and monitoring of his interactions with his daughter.
2. Three year olds tend to be rough on small animals, oftentimes they haven't yet developed the needed empathy or ability to modulate their impulses enough to be able properly handle a delicate animal, for instance -- they may get excited and wish to hug the kitten, or "play" with it by tossing it around, not being able to understand that its not constructed like a stuffed toy. That tendency goes away with gradual maturity and the best bet is to not allow her unsupervised time with any young animals and also to model (when able to) proper behavior with a young animal (petting, gentle holding).
3. If you are the primary caretaker and spend the majority of time with your child, model appropriate behavior and social skills, your child will follow along. The non-custodial parent will play a minor role, especially if he/she has conflicts with the non-custodial parents' behavior/thinking. But this comes in time. Some advice: DO NOT berate, belittle, put down, scorn or show ill feelings toward her father. No matter how "bad" he may be, he is her father and she identifies him as part of herself -- thus, you damn him, you damn her.
Finally, three years old is pretty darn young, relax and keep on the right path, I'm sure you'll do fine.