Your dog is acting like a puppy. At 4 mos old expect biting, and if you got her younger than 8 weeks, she didn't learn bite inhibition from her momma or littermates. You will have to teach her that then by letting her know that biting hurts.
As for alpha training, it is important that your dog recognizes that they are not on the same level as you. You are who they look up to and learn from. Just as a dog in a home with other dogs, one always tries to be the alpha. I learned with my dogs that by letting my yorkie up on the furniture, while not allowing my big dogs on the furniture, he took on the alpha role and acted accordingly. We cannot set pets on a path that they think they are human, they need to listen to someone for their safety if nothing else. I just don't think a little nip during play time shows that your angel thinks she is the alpha. Good luck!
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