I would not lay off the long term person, as it leaves you shorthanded and could affect your experience rating (i.e., dramatically increase the amount of unemployment taxes you pay). It could also open you up to an age discrimination suit (depending on the size and location of your business).
You don't mention what type of positions these are or where your business is located (both relevant to the various options I might recommend).
Assuming these employees are something other than minimum wage unskilled labor jobs,
assuming that they are not working under an employment contract or bargaining unit agreement, and
assuming that your business is operating in an "at will" employment state . . .
I would call both people in together and properly mediate an agreement where both parties commit to not let their personal feelings toward each other spill into the workplace again - ever. No more issues or episodes - period.
Explain that this unprofessional behavior is costing you time and your business money, and if it occurs again, there will be consequences -- specifically, that you will move both of them into a lower pay grade (which is totally justified, as the difference between, say, a "grade 2" and "grade 3" worker in whatever job they're doing is the amount of supervision required -- and you're having to provide WAY too much for them to be considered top grade employees). Of course, re-grading means a corresponding reduction in pay (20 percent maybe?). The consequences should hurt
them, not just you. (If you don't have distinct pay grades for their positions, you can create them now.)
One risk there is that if problems continue, the employee who is the better worker will leave before it comes to that (because she is more likely to be able to get a job elsewhere) -- then you'll be stuck shorthanded and one worker will have succeeded in chasing the other away (and she may do the same to the next worker if she doesn't like him/her).
To keep that from occurring, make it clear what your expectations are for "courteous and professional" behavior, and then closely monitor their actions. Praise them when they behave appropriately toward each other. But if an issue erupts because one person clearly ignored those stated expectations, don't punish both. Instead, provide a verbal warning to the offender stating that if it occurs again, it may be cause for termination (be sure to document the warning). If it happens again, provide a written warning, again clearly stating that another occurrence could result in termination. Although it will probably never go that far, if it happens a third time, issue another documented warning and send the person home for the remainder of the day with instructions to decide if she really wants to work there or not. If it happens a fourth time, terminate the person immediately -- and be sure to document that fact that she had at least five chances to comply before you took that action, but refused to do so.
Obviously, if these employees have some type of employment contract that specifies their wages or salaries, or if you're not in an "at will" state, then you'll need a different solution -- but I hope this is relevant and useful to you. Good luck.
