Your assuming that a client kingdom and a protectorate are the same thing. That's not the case. I can think of 2 instances when 2 competing large states both protecting a smaller one at the same time. Egypt is the first that springs to mind it was a protectorate of the Ottoman empire and Great Britain at the same time between 1882 and 1914. The second one is when Hungary and the Ottomans protected Wallachia and Moldova in the 15th century.