someone has recorded and voice overed my goat on my property without permission.. they even have my goat cursing.. i am not ok with this..

A cursing goat is no laughing matter...well, okay...it is kinda funny.  However, your question focuses on what rights you have to your goat's image.  Legal rights to images are generally protected under copyright law.  Copyright law provides the exclusive legal right to an originator to prevent (or allow) others from printing, publishing, performing, filming or recording literary, artistic, or musical material.  Accordingly, your goat must fit under one of these categories, i.e.: literary, artistic or musical material.  So, unless your goat is a sculpture that you crafted, you have no rights in your goat's image.  However, there may be other legal theories under which you can seek relief.  For example, if the baaaaaaad kid (double pun intended) trespassed onto your property to take the video, you could have a legal remedy under the torts of trespass to property or invasion of privacy.  Also, if the video of the cursing goat is intended to injure your reputation by exposing you to hatred, contempt or ridicule, you could have a legal remedy under the tort of libel. Depending upon the exact circumstances, remedies may also be available under the torts of slander or defamation. One interesting note: the hoodlum who got your goat cursing now has a copyright in their original and dubbed recordings.