Good evening and welcome. I am truly sorry to hear about this difficult situation.
Unfortunately, though, you are correct that this is not an actionable hostile work environment. That's actually a term that has a very specific legal meaning. Most attorneys are unaware of this, but hostility is only illegal in the workplace if it relates directly to a legally protected trait, such as race, religion or disability (i.e. yelling racial slurs). Being generally rude, disrespectful, insubordinate or conniving doesn't violate any law.
Along these same lines, an employee cannot refuse to work with someone because that person is engaging in hostility that does not meet the legal definition of a hostile work environment. Employers remain tremendous control over how they can run their business, including what personnel assignments they give their employees. You can advise your employer that you would prefer to work with other people, you can even quit if your employer is forcing you to do something you don't want to do, but you cannot force your employer into giving you a particular job assignment. They are free to direct you to manage whichever employees they deem necessary to run their business.
Now, as a practical matter, if there is written proof of this employee's intention to undermine you and "get you fired," most employers would take action against such an employee. This sort of backstabbing behavior has no place in a productive work environment. Especially given that this employee is new and your subordinate, most employers would be quick to take action against such employee and remove them from the company. But no law requires employers to manage their business in this way. While it would be completely counter productive to keep this sort of employee, an employer is free to run their business poorly, even into the ground if they want to. All you can do is appeal to their sense of fairness and what is in the best interests of the company. Ultimately, you would not typically have any recourse through the court system.
I hope that this addresses your concerns. If I can clarify anything at all, just let me know. If I have answered your question, I would very much appreciate a positive rating of my service so that I may receive credit for assisting you.
Very best regards,