If you were the president of Palestine?

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how would you handle the escalated events between Fatah, Hammas, and Israel?

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I would forcefully get rid of the radical element (a.k.a. Hamas, Islamic Jihad, most of Fatah, etc.) I would make sure that there are no militant groups in the country, other then the army and the police.
I would stop the nasty propaganda against the Jews and Israel. I would say to Israel "look, we have had plenty of disagreements, and we still do, but I don't want to kill you, I want for my people to live side by side with your people and I want for all of us to prosper. Enough being enemies! Lets build a friendship!"
I would invest into the education of my people, into farming, into hi-tech, roads, social services... Most of those things I could partner up with Israel on. I would later, as time goes by, and there is a lot more trust and isn't any killings, argue the borders of my country in the international courts, but I would also understand that Jews must have their Western Wall to pray next to, and that Jerusalem is truly a holy city to them, so I would keep that in mind while debating those territories.

Once Jews see a true partner in me, they would lighten up and rush to come to an agreement with my Government.

I would establish a democracy in Palestine, but the kind that doesn't tolerate any kind of religious, or other kind of fanaticism.

We would become the most peaceful and happy region in the world. Our armies could train together, our merchants could have joint businesses, our kids could go to the same summer camps and learn to be friends from the early childhood.

Edit:
And for all of the above I got 5 thumbs down. I know those weren't from Jews.
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Well Israel is staying out of it for now. I would call for new elections. If I lost I would retire and seek assylum in the US, if I won I would press to wipe out armed groups not government authorized.
There has to be a meeting, supervised by leaders respected by all involved. And this meeting would have a deadline, and by the end of that meeting peace would have to be achieved once and for all. I would refuse to allow anyone else to have their life taken needlessly after all of these years of war, fruitless waste of innocent lives, for what? What have they been sacrificed for? More hatred and more killing, and all the finger pointing in the world can not undo what we have all lost. Hope, faith, belief in a future, security, safety. None of this fighting and killing in the name of anything seems worth it. I do not see the means justifying the ends, I see the hate and violence continuing until there is nothing left to fight for. I think we have lost more than enough, and I understand that there are those who think the losses should continue, for the "enemy". What does that solve? Does that make us righteous in the eyes of G-d? I do not think so.
I would tell Fatah and Hammas to straighten up, the Jews are getting a kick out of them fighting each other.