First, a few points of clarification in your question from a legal standpoint. This answer assumes that you are a minority equity holder in a Florida limited liability company. As such, you are technically referred to as a "member," not a "shareholder," just to kept the terminology accurate.
As to your opening statement, there is generally no right of a minority member to mandate that the LLC operating agreement ("OA") be revised (indeed, in some instances an LLC OA may require a unanimous vote of the members to amend). Any exception to this general rule would be found in the LLC OA, but would be highly unusual.
Moreover, to your last point, members are not technically "fired" from the LLC; however, members often serve in the additional capacity (wear a separate hat) of an employee or officer or independent contractor for the LLC. The relationship among members (as members) and the LLC is governed by the LLC OA, the Florida LLC Act and common law principles. Under certain circumstances, a member may be forced to "withdraw" from the LLC or have his/her membership interest "redeemed" by the LLC and/or other members. While there are some common scenarios under which a withdrawal or redemption may be mandated, LLC OAs often have varying and unique provisions governing such matters.
Any other capacity in which a member may serve the LLC (as an employee for instance) may also be addressed in the LLC OA, or may be governed by a separate contract between the member and the Company; and, that contract may or may not be in writing. Therefore, the LLC through the majority vote may have every right to "fire" you as an employee, depending upon the form and content of your agreement with the LLC as an employee.
BUT, your membership interest is a separate interest protected under and subject to the aforementioned laws (LLC OA, the Florida LLC Act and common law principles). The fundamental starting point in addressing your concerns is the LLC OA and any other agreements to which you are a party in any other capcity with the LLC or the other members. You have raised several complaints of potential wrongdoing on the part of the majority members that may give rise to claims for breach of contract (i.e., the LLC operating agreement, or an employment agreement) or, stictly in your capacity as a member, for breach of fiduciary duties. There are possible issues - among other legal principles - of the majority engaging in self-dealing, wasting LLC assets and oppressing the rights of the minority member (i.e., you) to his/her lawful share of the LLC profits or other benefits afforded the membership. Your remedies for such wrongdoing, assuming the majority's liability for same can be proven, would generally be governed by the LLC OA, the Florida LLC Act (and, possible other statutes), and common law. You may be entitled, if successful, to money damages or equitable relief (such as, a judgment requiring the majority to refrain from doing some act, or requiring them to do some act, or possibliy even requiring them to purchase your shares at fair value), or both.
Again, the basic starting point to evaluate any potentials claims (and, thus, possible relief) is for a business attorney to review the your agreements. In the absence of an operating agreement, the Florida LLC Act will govern the relationship among the members. Moreoever, if the operating agreement is silent on an issue, applicable LLC Act provisions will govern. There are also certain provisions under the LLC Act that cannot be "contracted" around, i.e., some provisions of the LLC Act will apply in all instances regardless of any otherwise conflicting provisions in the LLC OA.
Even if the majority are, technically, acting within the provisions of the OA (i.e., they are not in breach), they are not immune from potential claims of breach of fiduciary duties to the LLC, duties which are for the benefit of ALL its members (namely, you as a minority member).