You can certainly make a Motion that he be required contribute towards your attorney fees, but usually that will not happen until the case is over. It is unlikely that the court would require him to mediate without his attorney.
The other attorney is correct, but there are other ways to get help with this. You can check out legal aid and other legal resources in your community. Call your county bar association and ask what resources there are.
You can also take it upon yourself to be prepared for the mediation and any and all court proceedings. There are lots of legal resources available for free in the court's law library, from Nolo Press (both their books and their web site are very good and comprehensive), your local library, and I've written a couple of books on this subject. If you prefer to purchase these books, you can usually find them online at a used bookstore for a reasonable price--I know that Your Divorce Advisor is usually available for 75 cents at half.com, for example.
Don't be intimidated by his lawyer. That's just how lawyers are. They are pushy. The judge won't like it that the lawyer is trying to push you around, so let him be a jerk to you.
But you need to take responsibility for getting yourself prepared and organized for all of this.
I'm not your lawyer and I'm not admitted to practice in NC so take what I say with a grain of salt. Use your best judgment, and your lawyer's best advice.
He is entitled to have an attorney with him at mediation if he so chooses and the Court cannot force him to go to mediation without one. However, you can make a motion for temporary attorney's fees and all three family judges in Sarasota would entertain that and likely award you some temporary fees if the income disparity is actually as great as you say it is. You should hire an attorney first to file and argue the motion on your behalf. This way, you both can be represented at mediation.