In her working hours, Melissa G. King administered benefit funds for the sandhogs’ union, associating with the muscled and plain-spoken men who blast through earth and darkness to build tunnels beneath the city. But in her free time, she squired her teenage daughter to the nation’s elite equestrian events, building a stable of horses that would be the envy of any on the horse-show circuit. The two worlds could not be more disparate. But to hear federal authorities tell it, she gained entry into one only by stealing from the other. Ms. King, 58, was charged last month with embezzling...