If the court required a certain mediator then no, if not she probably can ask for any mediator she wants but you will both have to agree on one.
Arnold & Wadsworth
If the mediator is court-provided, she could ask for a different one, but there's no guarantee the court would grant her request. However, mediation is a non-binding process. Even if she's unhappy with the mediator, she is not obligated to agree to anything in mediation.
Mediation may be court-ordered, but often the parties are required in the Order to contact a court-annexed mediation program, at which point they are either assigned a mediator from a list of neutrals or assigned a mediator that they jointly request. If there is some impediment to neutrality (i.e. if the mediator and one of the parties are related, former roomates, friends - or if the mediator has lost or given the appearance that he or she is no longer neutral by, for example, saying something that would suggest a bias in favor of one of the parties during a former mediation) then he or she should not be assigned to the case - and if already assigned, it would be appropriate for a party to request that the program director or coordinator assign a different mediator.
A weekly guide with tips and legal advice for each stage of the process.