The plumbing lines are run in the belly and branch off to each fixture. Having water at one fixture but not another is fairly common since it is likely that the "branch" that feeds the kitchen sink is frozen. While PEX pipes are fairly flexible and not prone to burst, the plastic elbows and fittings are, so you need to try to keep the heat going and watch for leaks.
First and foremost, you have to run the furnace, and run it a lot and at a higher temperature than you normally would. This is the only way to keep enough heat in the belly area to limit or prevent frozen pipes. The water lines are run next to the flexible mylar heat ducts in the belly, so the radiant heat from the ducts will help keep things above freezing. The heat has to be moving through those ducts to evenly distribute the heat. Do not rely on electric space heaters or the electric fireplace for heat in the main living area or in the belly (aside from it being a fire hazard), the furnace needs to run long and often, and yes it is going to consume a lot of propane!
Lastly, a bit of a physics lesson; the greater the difference in temperate between two objects, the faster the rate of heat transfer. To put this into real world practice, hot water pipes will always freeze before cold water pipes.