Boy, she is testing you, your limits, your dogs, and especially your reactions. She wants to see how this new life will be, so she is trying everything she can think of to figure it out.
The best thing to do is to talk softly and calmly to her when she is in er cage. When she is out and getting into trouble, have her step up, and praise her lots when she does. If she bites you, tell her sternly, no, no bites and don't give in to her attempts to get you to go away. If se won't step up onto your had, try a perch or stick and still praise her, or entice her up with a treat that you make a yummy big deal about.
Keep us posted, but for sure, discourage any interactions with the dogs, one day, they may retaliate .