No law prohibits rudeness or embarrassment in the work place. The laws against harassment and creating a hostile work environment only apply if the harassment is on the grounds of some protected class, including sex, race, sexual orientation, disability, and national origin.
Nothing you have described here will serve as a sound factual basis for a legal action against your employer or your supervisor. However, you are most likely an at will employee and if so, you are vulnerable to termination based on the on-going clashes with your supervisor.
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You would need to demonstrate that her behavior against you is related to a protected characteristic like your race, gender, or religion. The only other issue I see is her shoving your chair. An employer has an obligation to provide a violence free workplace. Shoving a chair might not be violent per se but it's inappropriate and your employer should not permit it. If you feel physically threatened by your supervisor because of the chair shoving then that may create an employment law issue.