I video taped my wife push me away from her. Sheriff saw the video and arrested her for DV. They want the video. Do I need to provide it to them?

If they get a search warrant you will have to provide the phone so they can obtain the video. The search warrant likely will allow them to take the phone until they locate the video. They may ask you for your password. You are not required to give it to them but without it they will keep the phone much longer. If you voluntarily offer the video they may work with you so that you are without your phone for a shorter period of time.  Of course, you MAY be able to get them to agree that if you email the video to them they will consider that enough and not search through the rest of your phone.  But you have no obligation to cooperate with them unless they have a warrant.