I am going to assume that the beach condo was solely in your mother-in-law's name. If the terms of the verbal agreement are not stated in the will, then those terms are not legally binding on anyone. So, the administration of your mother-in-law's estate should be straightforward, which is the collection and liquidation of assets, payment of claims, and distribution of the remaining proceeds equally among the three sons.
The executor has the power to sell the beach condo. As indicated above, this is what he supposed to do unless all three brothers agree to another arrangement like a buy-out or transferring title to the names of all of three brothers. So, hopefully, the brothers can make a deal.
In most jurisdictions, when the estate is going to be closed, legatees are entitled to review an accounting of the estate and be given notice from the executor of the hearing to close the estate so they can file an objection.