No, as long as the property is deeded in joint tenancy with right of survivorship, if one dies and the other is still living, the one living automatically becomes the sole owner and the property is not subject to probate.
There are essentially two kinds of joint tenancy in Florida, Joint tenancy with Right of Surivorship and Tenancy in the Entirety, which is used solely for married couples and is usually automatically deeded that way to married couples unless they request otherwise. Tenancy in the Entirity is the same as Joint Tenancy with Right of Survivorship but it adds a further protection to the couple that joint tenancy alone does not: creditors cannot get access to one spouse's interest in the property to pay debts unless both spouses are on the same debt obligation. Many but not all states allow tenancy in the entirety for real property in the state.
The issue OP has is that the property was likely deeded as tenancy in the entirety when his sister and then brother-in-law purchased the timeshare (the deeds typically state that the transfer is to the named married couple as "Husband and Wife"). By law in Florida, the divorce automatically changed that status to Tenancy in Common between OP's sister and former husband, which has no survivorship rights -- each owns a 50% interest and, if one dies, the property has to go through probate unless something was done to change the deed before death.