The original English text for the excerpt you’ve given above is:
And when you go into her room, don't forget to say, good-morning, and don't peep into every corner before you do it."
So here “peep into every corner” was translated 东瞧西䐐. It’s a fairly true translation.
In conversations, it is true that, for idioms, people favor ju1.
Actually, there may not be a consensus.
Try look up 教育部重編國語辭典 yourself.
It has ce1 for 螳臂當車, but ju1 for 杯水車薪, contrary to your suggestions!