JOEL - Once a chapel has been dedicated and set apart for worship services, still or video cameras are not allowed to be used there, except perhaps under very unusual circumstances. Chapels are considered a sacred place, like the temple, where the spirit of God dwells. It is out of respect for Him and the sacredness of the place that cameras are not allowed.
For civil marriages performed in a church, the Church Handbook of Instructions states:
"Civil marriage ceremonies should be simple, conservative, and in harmony with the sacredness of the marriage covenants. There should be no extravagance in decorations or pomp in the proceedings. Video recorders and cameras may not be used in the chapel."
Sometimes video cameras are set up to carry church services, like a stake conference, to other TV sets in the church when a very large crowd is expected. This is a rare exception.
If you had the ceremomy in any other part of the Church building you would be able to use the video camera. If you do decide to have it in the chapel you might be able to at least record the ceremony on an audio tape player. You would have to ask the Bishop. When Richard Dutcher, the LDS movie director, filmed the movie, "Brigham City", he was not allowed to use a functioning LDS chapel for filming an LDS church service scene. He had to use a building that used to be an LDS church but was purchased by the city for a different use.