I am a tiger in a relationship with a rooster, we have a dragon daughter... Will we all get along?

Yes, if you all work together, you can make a happy family life.
Well, as for you and your husband, the chinese astrology shows that Tiger and Rooster will argue a lot. They seldom want the same things. Each of these signs is strong of character. Both prefer to control the situation. If they can find a common ground, they can have a wonderful relationship. Thus, I suggest you both find interest and happiness from your child.