Let's not play word games. There are several million people living in that part of the ME, you admit that they're a cohesive political entity, and they call themselves Palestinians. They cannot be parceled out to the neighboring countries, because they're not Jordanians or Syrians, or whatever.
You can call them whatever you want, but in effect, they are the "Palestinian people," and many of them do in fact have a heritage in the area that predates the formation of Israel.
Thus we have a large, politically cohesive entity in the region, whose "statehood" claims can be justified on the basis of the same 1948 resolution that created Israel -- though the behavior of the Palestinians does not at present justify any sort of self-rule.
These are the realities on the ground: the Palestinians are for all intents and purposes "a people." They are too numerous to be relocated, especially since nobody wants them. They are led by murderers. They may or may not be capable of becoming civilized.
If they cannot be civilized, then there is no option but extermination. Because extermination is not an acceptable option, we must procede on the assumption that they can be civilized -- and there is no reason to suspect that, absent their murderous leaders, the Palestinians can't behave peacefully.
The Israelis have been attacked several times, but they have won all the wars, and as a result have gained additional land. This the way these things work.
Arab nations (such as Saudi Arabia or Jordan) typically do not allow Jewish temples or Christian Churches. The Moslems have a habit of excluding "the other team". Why do the Jews have to bend over backwards to create a nice, tolerant environment for the "Palestinian people"?
All people who self-identify as "Palestinians" are terrorists, in my opinion. I support Israel's war against Terrorism. I wish that the US would actively get involved. There is already blood in the street. More of that blood should be "Palestinian".