One question would be, was the fenced in area locked... Nonetheless, the police may use "reasonable" force to effect an arrest. Whether the arrest is valid is a completely different question. However, if the police used excessive force and also violated your constitutional rights and you sustained injury resulting in damage, you have a claim in tort and possibly a claim under 18 USC 1983. This is a very complicated area of law that should be fought in Federal Court.
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The police can enter your home to execute an arrest warrant. They may take the position that this was your home because it was your trailer in which you were living, even though it was in girlfriend's yard. Once they seized you, they could probably enter the trailer to do a security sweep, looking for other people in the trailer. They would not be permitted to do a full search of the trailer, however, without a search warrant. Since these issues depend on the particular facts, you need to discuss them with a lawyer. Also, the police version of what happened is likely to be very different from yours.
This answer is provided for educational purposes only and is not intended as the practice of law in any jurisdiction in which I am not licensed. The answer does not constitute legal advice nor does it create an attorney-client relationship. The answer is based only on the information provided, and may be inaccurate in the context of additional facts that have not been provided. The questioner should be aware that I am only licensed to practice law in the state and federal courts of Minnesota. Accordingly, before taking any action or refraining from taking any action, the questioner should consult with an attorney licensed to practice in his or her jurisdiction.
Your question does not mention why you were arrested. Did they have an arrest warrant. If so, and it was reasonable to believe you were in the trailer in the backyard they could enter the backyard. If they did not know that you were in the trailer you have an expectation of privacy in the fenced backyard that you were staying, and they could not enter without an arrest warrant, search warrant or consent.
Excessive force to effect an arrest is another issue.