Michael Andor Brodeur’s picks for the weekend’s TV offerings, including “Doomsday Preppers Bugged Out” on Saturday at 10 p.m. on National Geographic; “A Nanny’s Revenge” on Saturday at 8:30 p.m. on Lifetime; “Billy the Exterminator” on Saturday at 10 p.m. on A&E; “The Amazing Race” on Sunday at 8:30 p.m. on Channel 4; “The Real Housewives of New Jersey” on Sunday at 9 p.m. on Bravo.
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