One of the fundemental axioms of political science is that Liberal Democratic States do not go to war against each other, since Democracies will resort to both intra-national and international democratic institutions first. So, if Canada and the U.S. have a dispute over lumber, Ottawa doesn't send a flotilla of ships to bombard Washington, D.C. They go to the World Trade Organization and argue over treaties. Congresses of both nations act. The respective State Departments of both Countries keep relations normal.
A necessary corollary is that force of arms is necessary against Non-Democratic States and Entities who do not participate or recognize legitimate international democratic institutions. There are few effective checks against the leaders of totalitarian regimes.
The "pre-state" of Palestine is almost a Democracy. Palestine has a smattering of democratic institutions. One indicia of a democracy is that the entity has two peaceful changes of political leadership in a "free and fair" election. While the election of Hamas to power was free and fair, it does not seem to be a "peaceful" transition. There were riots in the street by the opposition Fatah party supporters. Fatah members have been calling for the resignation of their leaders and threatening to kill Fatah politicians who would join a Hamas government. There also have been several gunfights between Hamas members and police, leaving four officers and a Hamas gunman wounded.
Another indicia of a democracy is that the people who vote hold democratic values. One of those values is respecting the territorial integrity of neihboring states and entities and resolving border disputes non-violently by resorting to diplomacy. Of course, the people of Palestine have elected Hamas into power, which is considered a terrorist organisation by most of the world, since it is committed to the utter annilation of its neighbor Israel.
Another value is peace. Hamas is an organazation that wants to wipe Israel off the map. Hamas does not recognize the State of Israel. Hamas has not been willing to renounce violence or suicide bombings or the killing of Israeli civilians. In short, nothing Israel can do will make Hamas happy, except leaving the land of Israel.
Palestinian voters elected a party with these views to office! Palestinians KNOW what Hamas stands for. They understand that Hamas wants to destroy the State of Israel. It is not just Palestinians looking to change a corrupt government. If you want to get rid of a thief living in your house, do you throw out the thief and invite in a mass murderer who kills innocent civilians, olympians, and children on purpose to make a political statement?
There is something fundementally wrong with the Palestinian outlook that kills any prospects of Democracy. When a Palestinian child is killed by the Israeli military, 999 times out of 1000 it can be explained away as an unfortunate mistake or legitimate collateral damage of a focused attack against a military target. When an Israeli child is killed, it is done on purpose, with the thought of creating maximum grief and suffering against the civilian population.
There is a reckless and criminal indifference to human life that is tolerated by Palestinians. This attitude needs to be changed if there is ever to be hope and democracy in the Middle East.
So, how should Israel respond? Intelligently.
Since Israel is dealing with an enemy CLEARLY COMMITTED TO ITS DESTRUCTION, Israel needs to destroy Hamas. The time for playing nice is over. By electing Hamas into government, the Palestinians have declared war against Israel. Israel should respond with complete and overwhelming force. Crush it. Kill all the leaders and party members. Wipe out the PA entirely and start from scratch. Then, Peacefully and Humanely relocate all Arabs and Palestinians out of Israel and move them into a clearly defined Palestinian territory. Heck, even pay them compensation. Why can Arab countries expell Jews but Israel can't expell Arabs? Redefine the borders of Israel and make the Palestinians live with what they got. No more swiss cheese borders. People have no right to live in a State which they do not support. End of Story.