I received a call from the mediator stating that the other party's attorney has another hearing on the date we agreed upon. I believe it is a stalling technique , being used by the other party's attorney due to things not going the way they expected. Doesn't both parties have to agree on a date? The mediator told me it was changed to another date they didn't ask was I available for that specific date.
If you can't make it, be up front about it and focus on finding a date on which all parties can sit down and attempt to resolve the disputes. Fundamentally mediation is a voluntary process--no one can MAKE someone else agree to something, or even attend, a particular mediation. Don't go there with "I believe it is a stalling technique" -- people have conflicts that arise all the time and need to cancel appointments, especially lawyers, since it is the court that tells you when the hearing is, and you have to go. Keep your eyes on the prize--in your case, resolving a custody dispute instead of giving up the power to decide it yourself and having the court to decide it for you--and keep working to bring the parties together on a particular date so that it is possible for agreement to be reached.
Not legal advice as I don't practice law in Florida. It's just my two cents on the facts you describe in light of general principles of law. If you need legal advice, please consult a lawyer who holds Florida licensure. That's not me.
Lawsuit / Dispute Attorney
If this is a mediation to a pending lawsuit, then someone should be filing a notice of mediation with the court telling the court that everyone agreed to mediate at a specific time and place. The mediator can file it or either party can file it. Of course, that's no guarantee that things can't change later, but it creates a record; and, the party with the conflict will have to file an amended notice or risk possible sanctions for not appearing at the first agreed time. Next time you have an agreed time to mediate - make sure the mediator sends out the notice or just do it yourself.
Divorce / Separation Lawyer
I agree that conflicts do sometimes arise which require the changing of dates for mediation. I have unfortunately seen attorneys misrepresent their schedule in order to delay the inevitable. I would ask the attorney to advise the case number, matter name and the time and date of the alleged hearing. You can then look it up online to determine if they are telling you the truth or not. If you discover that the attorney is not being truthful, I would file a Motion to Compel Mediation.