Notwithstanding any other provision of law, all violations of statutes, regulations, executive orders or rules relating to the operation of any vehicle in the District, including rules issued pursuant to Chapter 14 of Title 8, except those violations covered by subchapter III of this chapter or those violations excepted by §§ 50-2302.02 and 50-2302.03, shall be processed and adjudicated pursuant to the provisions of this subchapter. All violations of regulations issued by the Capitol Police Board, pursuant to § 10-503.25(a), that if committed outside the United States Capitol grounds would be covered by this section shall be processed and adjudicated pursuant to the provisions of this subchapter.