Precedent

There is an interesting precedent for the situation between Israel and its two enemies, the Palestinian Authority on the West Bank and Hamas in Gaza. Once the country of Bangladesh was known as East Pakistan and West Pakistan is what we now call Pakistan. The two unequal portions of Pakistan were joined by their Muslim religion and their hatred of Hindu India from 1947 until 1971. But, as often happens, two discrete parts of one country cannot remain joined in perpituity. Not only were East and West Pakistan separated by distance (1,500 miles), but more importantly they were separated by language (Urdu in the West and Bengali in the East) but also by political and economic interests. The people in East Pakistan felt that they were being dictated to and exploited by their more powerful Western colleagues. This lead to demonstrations, political ferment and ultimately civil war. The armed forces of East Pakistan were no match for the forces of the main army of West Pakistan, but what made the difference is that India intervened on the side of the East Pakistanis and without Indian help in defeating the Pakistan army and providing economic aid, Bangladesh would not then have come into existence.
What relevance does this situation have for the Israel-Palestine conflict. In some ways the situation is reversed. The distance between the two halves of the Palestinians is much less in this case (only ca. 50 miles) but in a physically separated "country" distance really does not make much difference. Nor in the case of the West Bank and Gaza does the language make any difference, they both speak Arabic. But, the political differences are profound, Fatah of the PA has taken the fundamental (and supposedly irreversible) step of negotiating with Israel in a peace process, while Hamas totally rejects any contacts with Israel. Their stated policy is to destroy Israel and replace it with Palestine.
The crucial point here is that while both sides in the Pakistan-Bangladesh conflict hated India and regarded it as an enemy, when it came to a clash between themselves Bangladesh was glad to accept the help of India. Not only that, India had no territorial claim to Bangladesh, and indeed did not want to become responsible for 120 million poverty stricken Muslims.
The precedent then is that in this case, Fatah, while hating Israel, might well be prepared to accept Israeli help in order to overtake Hamas and rejoin Gaza to the PA. Now it's true that in the India case, the Eastern part of Pakistan wanted to be separate, while in the Palestinian case the West Bank wants to be rejoined with Gaza. While in the long run we cannot tell what will happen, nevertheless the use of a hated enemy, Israel, by one side, Fatah, to attain Palestinian national goals is not beyond the realm of possibility in the current situation.