This is a perfect example of what's so bad about things like indoctrinating children (yes, this reaction of your's is essentially the same logic): You apply broad generalizations about a perceived evil "other side". Black/white thinking and taking anything bad the "bad side" does as a reason to claim "all of them" do. Throw in a nice portion of "who is not with us is against us", and you got a nice hateful hawk cocktail.
First, you implicitly stereotype all Arabs/Muslims suggesting they all support Hamas, and next, you blame all of them collectively for these children videos, for the sole purpose of hating them better and rally up support for your calls of war against them. Ironically, Hamas does the same by blaming all Jews collectively for civilians killed by the Israeli army, and by ripping these deaths out of context, for the sole purpose of hating Jews better. Hell, even horrible crimes in the past would not have been possible without such a kind of hateful stereotyping.
When will people ever learn that stereotyping for the purpose of hatred and war will not give us a way out of this conflict?
Both sides have legitimate concerns: Israel wants a sustainable peace and security, and Palestinians want a state and freedom from occupation. Now you can argue that the Palestinian side is doing much less than the Israeli side for compromise or for finding a solution, and that may very well be right. You can also blame Hamas for this despicable indoctrination of children. But don't fool yourself, in any conflict, both sides engage in stereotyping, black/white thinking (have you ever met a party in a conflict where people believed they are not the good guys?) and I pretty sure quite a few Israeli parents will teach their kids similar things about the Palestinians, even if there is no TV program of that kind.
Playing the eternal blame game will never solve this conflict. Hell, it doesn't matter at all who "started it" in the past, if you want to find a solution for the future. Perpetuating this stereotyping villification of the "other side" and hatred only puts more fuel into the flames. We shouldn't contribute to that, should we?