Ah yes another Israeli showing their true colours and equating all Palestinians to Hamas. Nowhere in the motion did it indicate that Hamas would be legitimized. The motion did call for recognition of Palestinian statehood - if we accept that Israel has a right to exist based on the UN resolution, then Palestine has a right to exist based on the same resolution.
Now on to the nonsense about Palestinians rejecting the peace process. Remember, it was an Israeli who assassinated Yitzhak Rabin, thereby derailing the Oslo accords - there is some evidence that Shin Bet (the Israeli secret service) was aware of the threat on Rabin's life and stood by. In 1996, the final nail was put in the coffin when Israelis elected Netanyahu, knowing full well he was against the peace process.
The only conclusion that can be drawn is that it is in fact the Israelis who are against peace in the middle east, and this woman is simply projecting her views on the Palestinian people.
I am also not convinced this woman constitutes a minority in Israel. The majority of Israelis remain silent during the ongoing campaign against the Gazans.