Like you say, the propaganda of the West is relentless and difficult to get out of our heads.
I believe most could not care less about having a state of their own. All they want is to live in a safe place with opportunities. Also, Jordan IS Palestine. They don't want to pay to bring Gazans out of poverty especially if they come with terrorists in their midst.
As you so correctly point out, the violence obscures the desires of the majority for the agenda of a few.
Partly (again partly), everyone uses the canard that Palestinians want to kill all Jews and take over Israel as an excuse to NOT give them citizenship in a wealthy country. There are millions and millions of refugees all over the Middle East and in Turkey.
There are refugees coming into the U.S. They're everywhere and politicians do well vilifying them instead of finding a long-term solution. As you write on, about :)