It seems like the animal issue is an indication of deeper relationship problems, mainly lack of communication and her being a bit controlling. Even though pets can seem "silly" to some people, when you love something as much as you clearly love animals, denying you that joy is a huge hurdle in your relationship. While obviously you love her, it may be time to re-evaluate what you're priorities and goals are in life compared to hers.
I hope you can get her to open up and start talking!!!