I don’t agree Israeli support for a two state solution was higher than Palestinian support, if you are referring to the public attitudes. The Israelis activists pushing for a Palestinian state have always been a small, fringe minority within Israel. None of Israel’s political leadership have favoured a two state solution since 1995 after the assassination of Yitzhak Rabin, the last PM in favour of it, by a far right Jewish radical. One Knesset member did and he has been tossed out of Knesset for saying so.
The Israeli government and public resistance to a two state solution is justified by security concerns, with other additional unspoken concerns like not wanting to relinquish all the illegally seized land and displace close to a million illegal settlers.
The Palestinian Authority wants a two state solution, but Hamas do not. Most Palestinians want a two state solution, but currently see the PA peaceful way as a huge failure after almost 30yrs of nothing but worse and worse oppression and persecution under the occupation. The PA broke away from the PLO who had tried a two state solution under Oslo, but were badly let down by Israel not upholding their end of the deal. The PLO wanted to go back to terrorism, the PA were the Fatah moderates who wanted to keep trying peaceful cooperation. So, over time, the harsher Israel got, the more support grew for Hamas- I’m talking about the repeated military attacks on Gaza since 2001. Many now see armed resistance as the last resort. Interestingly, many think the reports of war crimes by Hamas are either propagandist lies or think it’s fair given the war crimes done to them by IDF. As in you fight fire with fire, safe to say Isrsel feels the same way and twenty years down the road everyone is being repeatedly burned. A similar number of Israelis are convinced reports of IDF war crimes are propaganda and they truly are the most moral army in the world.
As for who thinks they should have it all, that is clearly present within the Israeli far right government comments on ethnically cleansing Gaza, resettling Gaza, the increased seizure of private Palestinian lands. All you have to do is look at the recent history and changes to the landscape and maps to see who is in the process of taking it all.
Hamas also thinks they should have it all, but they currently have zero of it really, it is all under Israeli military occupation and martial law. There is no international support for Hamas governing any part of a nascent Palestinian state, so I’m not too worried that they’d end up in power.
There will need to be give and take to get to a fair division.