So we have to come to some sad conclusions. The Palestinians seem ready to do zilch to protect their children. They'd rather the children be martyred and make good propaganda than to cooperate in saving them. Something we already knew is that Palestinians are not very nice to each other. There seems to be little of the volunteer attitude of taking care of each other that we know from Israel. (I've known for years that even within Israel in Arab villages - where part of the population are "internally exiled" who were evicted from their villages in '48 - these people are still considered refugees and second-class citizens compared to the "real" inhabitants of the villages.)
The UNRWA and Red Cross will not touch a project that might potentially anger their Palestinian hosts - so while they are good at complaining about the humanitarian disaster that Israel has caused in Gaza - they won't move a truck to get children out of the line of fire. Palestinian/Israeli dialogue organizations won't disturb their brotherhood by helping with a project like this. The Palestinians are suspicious and the Israelis won't call them on their suspicions.
I've known for years that any cooperation with Palestinians demands - first-of-all - asking what they want us to do, and then doing it. They don't appreciate it when somebody - on their own initiative offers help. And they mostly don't let facts confuse them - Israelis are fascist racist murderers and they will do everything in their power to be sure their world looks that way.