2 Employees in a relationship, employer not informed

An employee asked could her friend apply for a position we had vacant, we interviewed her female friend and took her on.
We now find out they are in a romantic relationship, which causes a conflict, because they both work as cashier / checker and both handling cash. They have not informed us that they are in a relationship, but other staff are aware of the fact.
Now one of them is causing problems for us, changing her day off to be her partner, taking time off unauthorized, having a bad attitude to her supervisor,refusing to sign a warning letter issued to her,do we still have to go through the process to dismiss her,or both.

Of course, all employees have the right to due process. What I would suggest you do is to document every infraction that the employee commits. Follow the necessary procedure (NTEs and Decisions). That way, when his/her infractions reach the limit (termination), you have legal bases to dismiss him/her.