Do you have issued with some of your religious believes vis. a vis. language of the Oath?
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Private ceremonies are only done in very unusual and exigent circumstances, generally when the applicant is physically incapacitated and unable to attend a regular ceremony. The fact that you want to "speed up" the process so you can petition for your mother is not a sufficient reason. Everyone wants things to go faster then they do.
While this answer is provided by a Florida Bar Certified Expert in Immigration and Nationality Law, it is for general information purposes only and an attorney/client relationship is neither intended nor created. You should seek out qualified counsel to review your case and provide you with advice specific to your situation. Call +1-561-478-5353 to schedule a consultation with Mr. Devore.
You can contact the Federal District Court in Fort Myers and request a private oath ceremony but as my colleagues have stated that is a very subjective decision as USCIS and a Federal Judge would have to both agree to the process. In very specific situation, it has been done but it is a case by case determination.
Legal disclaimer: The statement above is provided by CC Abbott is based on general assistance and not intended to be a legal opinion because not all the facts are provided. The person requesting information and all others reading the answer should retain an attorney who is permitted by the state bar within the jurisdiction who can examine the complete facts and provide a legal opinion on your case. All information provided in the above answer and other information provided by CC Abbott does not create an attorney/client relationship within any state of Federal law.