Dear Customer (name blocked for privacy),
A determination of whether or not you must submit to mediation will depend not only on what the letter says, but, based on what you describe, prior conversations or agreements you may have had with these people, the trust, and even your father's will. Only an attorney who has thoroughly reviewed all matters in which you are involved can provide you with full information.
The sentences you quote, however, just from reading them alone, do not appear to say you must submit to mediation, they only indicate that if you do not agree to mediation then they will take you to court. But, again, other documents and involvements you may have may require you to submit to mediation, only an attorney who has full information of what you are involved in can tell you. The petitions they can file against you, again, require you to speak to an attorney who can review the facts, the trust, will, appraisal, your desires, the other parties' disputes or statements, and many other factors.
I am sorry I could not provide you with more information, but there are too many items which cannot be communicated in this forum, and which only should be spoken to legal counsel in your state whom you have hired to represent you. JustAnswer is here to provide information, not legal interpretation or advice - only an attorney hired by you can do that.
PLEASE NOTE: Responses here are for information/education only, NOT legal advice and do not form attorney-client relationship! Only licensed attorneys you hire in your state can provide legal advice.