In war collateral damage always occurs and it always has done.
War is between nations, hamas & co are little more than a semi legitimate terrorist organisation, the people and economy of gaza is not on a war footing with isreal (which would be a joke anyway), it is nothing more than occupied territory.
It's more a police action than a war, bombing achieves nothing, countless modern examples exist to show this. What little we achieved in Iraq and Afghanistan was not achieved by bombing.
According to you, that is entirely our fault (re. the IRA) and the fault of the Israelis (re. the muslim attempts to take their country).
If a terrorist French organisation attacked London, would you advocate bombing Paris?
Arguing fault is an easy trap to fall into, the question is "is the action appropriate" and "what does it achieve".
It may be the stupid Muslims "fault", it may be a morally or legally justifiable "war", but what does it achieve? Israel repeatedly retaliates against them, (yes, retaliate, not attack), yet every time all it achieves is a pile of dead bodies, a temporary truce, and even more reason, justified or not, for the other side to continue hating them.
how would you suggest that Israel go about finding a peaceful solution?
They have 3 options.
1. Wipe them from the map.
2. enact police action and not military action, then continually apply diplomat and economic pressure, the iron curtain defence system works so the attacks are generally ineffective, stop further settlement. Hamas would likely collapse at some point, some analysis already suggest they are at the point of collapse and almost need isreal to attack to create support for them. They will have to make concessions, and they will have to outlast Hamas (Hamas will never concede), yes, it amounts to waiting for a better option to present itself.
3. Do what they are doing, what they have done a number of times before, and what will happen again and again BECAUSE IT DOES NOT WORK.