Israel's government used the argument that Hamas exist -and so the National Authority isn't talking for all Palestinians

Have you got a source to back them up?

As far as I know, last negotiation (2014) collapse because of the announcement of reconciliation between the 'good' guy and the 'bad' guy.

Source (1)

Israel has hit back hard following an agreement on Palestinian unity by suspending already faltering peace negotiations just days before the expiry of a deadline for the US-brokered process.

The Israeli prime minister, Binyamin Netanyahu, accused the western-backed Palestinian president, Mahmoud Abbas, of forming an alliance with Hamas, which he called "a terrorist organisation that calls for the destruction of Israel" – and hinted at further retaliatory measures.

Source (2)

On April 23, Fatah and Hamas announced a new reconciliation agreement to form a technocratic government of independents and to begin a process to hold elections in the West Bank and Gaza. Israel responded by officially calling off the negotiations.

BTW, what I mean when I say 'negotiation' is not in the literal sense. Loosely, I mean 'to engage diplomatically'.