Part of the problem is that based on what you wrote is that you are an enabler. You roommate knows this. She has figured that she can away with it and that you will pick up the slack.
First you need to decide how important these issues really are to you and how committed you are to making a change. Are you willing to move out? Are you willing to stand up for yourself? Are you willing to walk away from the relationship?
I would suggest that you discuss the situation with the roommate and try to set up FIRM and FAIR rules about chores and responsibilities. If either of you can’t or won’t agree to follow the agreement then make it clear that one of you will move out. A lot depends on who signed the lease.
Do not let her bring her dog. The landlord will kick you out and keep your deposit in a heartbeat. As for the cat, if it is young I would seriously consider giving it up for adoption now. It will have a better chance of being adopted as a kitten then as a older pet. Hard to do but you seriously screwed up getting a cat and now it time to be an adult.