We have two employees who are in a relationship and one has told us he/she will file a restraining order and call police on the other, but we feel our hands our tied in taking any action for fear of discrimination based on our knowledge of the private situation. It is now making managers uncomfortable to be on shift with them. What recourse do we have at this time?

Are they employees "at will"

The one who might file a RO should be sat down in personnel and told firmly that that sort of personal and highly charged emotional matter is disruptive to the company and all employees, and any further mention of it will put him/her in consideration for termination - until/unless it happens. The court will decide how to handle the work situation. The wording, of course, will depend on COMPANY POLICY regarding warnings, probation, and termination. If you don't have such policy, it's time to do so, with a handbook for each employee, or put it online.

Do not allow for any rants about how dangerous this other person is - it's not your concern.

Make it clear in general terms that relationships outside the company are not welcome inside, unless they are on good terms, for the good of the company and it's people.

The company doesn't need to be held hostage to hiring and firing rights.

What's the company policy on workplace relationships? You could keep them on different shift while you sort it out, or fire them both if they have behavior that disrupts the workplace.

This is exactly why intelligent people don't play house with other coworkers.

Many places will fire BOTH for being a disruption in the workplace.

Both employees need to be talked to about bringing personal issues to work.

If there is not a policy about this, one should be written.

If possible, if there are issues, they need to be separated by departments or by shift

As long as you do not treat them different because of race, religion, and the few protected rights, why would it be discrimination? If they would be gay, just treat them like you would non gay couples with same issues.