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What you describe is NOT a switch loop like the diagram above. What you have is power comes into the switch box first. Then a cable goes fromt the switch to the light to feed power to the light. The other cable going to the dining room light supplies unswitched power from the power feed comming into the switch box. It's just pigtailed.
So, if you want to replace the cable from the switch to the light you can do that no problem. But you'll need to write down how all the terminations are made and then make sure you connect it back up the same way.
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