Palestine considers the entirety of Israel occupied palestine. If they didn't, they wouldn't be lobbing rockets into Tel Aviv nor would they have a blockade.
Israel and palestine lived peacefully side by side with most palestininans working in Israel and stable borders with no blockade until Yasser Arafat declared the intifada.
Here's why they are lobbing those missiles:
"The Israeli blockade of Gaza, established in June 2007, is a brutal form of collective punishment that violates Article 33 of the Fourth 1949 Geneva Convention, which set up rules for the 'Protection of Civilian Persons in Time of War.'
"The blockade has turned Gaza into a sliver of hell, an Israeli-administered ghetto where thousands have died, including the 1,400 civilians killed in the Israeli incursion of 2008. With 95 percent of factories shut down, Palestinian industry has virtually ceased functioning.
"The remaining 5 percent operate at 25 to 50 percent capacity. Even the fishing industry is moribund. Israel refuses to let fishermen travel more than three miles from the coastline, and within the fishing zone boats frequently come under Israeli fire.
"The Israeli border patrols have seized 35 percent of the agricultural land in Gaza for a buffer zone. The collapsing infrastructure and Israeli seizure of aquifers mean that in many refugee camps, such as Khan Yunis, there is no running water."
Chris Hedges: Elites Will Make Gazans of Us All - Chris Hedges' Columns - Truthdig
The period of relative tranquility you reference was partially undone when the USSR collapsed and hundreds of thousands of Soviet "Jews" moved to Israel and took the jobs of Arabs who were living in Palestine before the Jewish State came into existence,