FTR, maybe I'm wrong about this, but the impression that I get is that the extreme level of terrorism and violence of the Second Intifada caused many Israelis who were otherwise pro-peace to shift to the right in their political views; thus, I am wondering if this shift can be avoided or at least reduced in this TL.
The dynamics of internal pressire I don't think would have changed with a successor to Arafat. It is possible that Abbas, who was most likely the next in line at the time anyways, would not have acted as hamfistedly at Camp David, and I think that he understood a bird in hand was better than two in a bush. But the basic principle of not wanting to be the Arab leader who formally gives up a part of Jerusalem I think would get to Abbas as well, who to be honest would fear for his personal safety. I think Arafat was a bit more pragmatic than sometimes he is given credit for, but the failure to counter offer was a devastating blow to future relations.
The failure at Camp David I think was a true shock and did lead to a rightward shift. Barak was perceived as wanting to give up way too much, with the majority of the Israeli public and a good part of the moderate left thinking he was going beyond what he had any right to offer. It was probably a significant reason why Barak lost so badly in the prime ministerial election. But yes, the real rightward shift came in the next general election, and that stemmed from the Intifada and the feeling that the Labor Party wasn't taking terror seriously while Likud and Sharon were. The wall and the offensives in the West Bank legitimately did reduce terror.
The issue is transposing the conditions of 2000 with the ones of today. On some issues, things are much better. Israel has significantly less to fear from the Arab States, who other than Syria and Iran, pose little real danger to them. Security concerns on the borders are less of a problem. The water issues have gotten better, as well, as technological advances have made some of the old issues less significant. But the real crux of the issue at this point in time are the growing extremism of Palestinian rank and file political players, with Hamas in true positions of power now, as well as the expansion of the settlements, which are going to be a real bitch to evacuate if the issues with the Gaza evacuation of maybe 8000 settlers are magnified. The IDF is significantly more ideologically infiltrated these days from 2005 and refusal orders would skyrocket in such a scenario, while the settlers are better armed and less loyal to the state.