re: "Weep for these children, too." Many of us do.
It's called "the cycle of hate".
And you seem to be among those who perpetuate it by waiting for the other side to stop it, while applauding the side you're on in its continuance -- however "inadvertant" you claim that to be.
Believe it or not, there are also Palestinian and Israeli children who play together, and go to school together, because their parents are trying to break the cycle. Pray for them, too -- that they may succeed, and inherit.