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I am sorry for this dilemma.What you are describing is an abuse of police authority...specifically, there is no obligation for any citizen to speak to the police...and no obligation to "leave their home" to speak to them. If the police have probable cause, they can arrest someone...but they can not use force to make someone talk...that would violate the 5th Amendment of the constitution.
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It would be illegal for the police to enter your home without authority (an invite from you or a warrant, or an exception to the warrant requirement).