One of the first steps to lasting peace, is, as you say, for Palestinians to be given the same rights Israeli's in all aspects of their lives including the right to own property anywhere and not have it taken from them. That, or go back to a two state solution. Before the arrival of Islam, most of the Palestinians Arabs would have been Jewish - it distant relations fighting each other.If one set of people are occupied/under oppression/apartheid conditions with family members constantly murdered they will rebel against it (natural thing to do).
This is in the US and Israel's hands, they are the occupying force. They retain control. The US could broker a ceasefire and steps to peace, Israel would need to enter talks in good faith, because they hold the power and are likely to have to cede the most land due to settler violence and confiscation.
If the US and Israel aren't happy with Hamas, offer up an alternative. Negotiate with the PA (West Bank). Drop the blockade and occupation. They could do it in stages. The West Bank first (No Hamas), remove the check points (or at least remove the military from them initially). Allow integration, give Palestinians in Israel the same rights as the Jewish population. Investigate war crimes (both sides), hold people to justice. Some form of restorative justice (ala Truth and reconciliation commission in South Africa). Reparations for Palestinian victims and families. There are so many layers that need to be addressed for this to work - most require Israel to cede some power, which I don't think will happen. Esp with the current govt.