If the cartels took complete control of Mexico

So, in this situation does Mexico still have an economy? I assume tourism has stopped, but are they still a petroleum exporter? Do they still make cars and trucks for export? Do they still grow Avocados and sell them to the US? Because the Palestinians in Gaza don't really have an economy to speak of, so unless you first reduce Mexico's economy to something barely self-sustaining, it really isn't a fair comparison.

then stated their goal was to kill all Americans

Not much of a cartel if they're killing their best customers.

we might start patrolling our border a little harder

See, that's a key difference. Nobody's saying that Israel shouldn't patrol their own border. What's a bigger issue is that they're patrolling the other borders too. Israel is in a position to cut Gaza off completely. Israel can completely shut off water, food, fuel and power to Gaza. Even before this conflict they shut off tourism and fishing.

In your scenario, imagine the US Navy had carrier strike groups in the Gulf of Mexico and along the Pacific coast, preventing even fishing boats from leaving the Mexican shores. Now imagine the Guatemala and Belize borders were closed too, so that the entire country of Mexico was essentially a prison. That's the situation in Gaza.

Also, in your scenario, is the US government encouraging Americans to move to Mexico and set up little American compounds there, either by building their own houses or by kicking Mexicans out of theirs and moving in? When Americans go to Mexico and take over a Mexican house, are those Americans protected by the US military? And do they get the protection of US laws, as if the families still lived in the US?

there is a reason that Israel is in the West Bank in the first place

Yes, they have extremely unfriendly relationships with almost every neighbouring country, and they seized that territory after one of the many wars with those neighbours, and have continued to occupy it counter to international law. That, of course, leads to extremely unfriendly relationships with almost every neigbouring country, which leads to conflict, which leads to a need to try to control that territory.

there will never be peace in that region until Hamas is stripped of all power in Gaza

And Hamas (or a group like Hamas) will always be popular in Gaza until people in Gaza have a reason to stop hating Israel, which will only happen when Israel changes the way it treats them. But, Israel is unlikely to treat them better because they know that the people there support Hamas (or groups like Hamas) because of how Israel treats them.