A jarring split-screen reality will come into focus this week, highlighting grand American ambitions internationally amid political dysfunction back home. As the U.S. and China compete for influence, two cabinet members are making yet another trip to the Indo-Pacific, a region with vital naval hubs and shipping lanes: it's the 12th and eighth trip there for the secretaries of state and defence. Meanwhile, at home, the U.S.'s notoriously bitter domestic politics is spilling into international issues in novel ways — with battles over abortion and LGBTQ issues stalling everything from U.S. military hiring and promotions, to diplomatic appointments and a…