I do get your point fully! However, PKK, and Hamas are two different entities. We could probably agree, or disagree with each other but let's be frank here. Hamas won the legislative Palestinian election in 2006. Perhaps Turkey like many countries in the East does not stamp Hamas as a terrorist organization, and that's why the reason why Turkey is not fulfilling the demands from Israel.
When it comes to Israel's support to PKK then we find Israel looking out for its own interest by weakening neighboring states in the region. Israel has been very on and off when it comes to supporting PKK "openly", however, we have many reports indicating that Israel has been training PKK in especially Iraq. Israeli intelligence has assisted PKK in penetrating a country and executing a successful terrorist attack.
However I get your point is not specifically about Israel, but more about the morals&etiquettes of the Turkish state, and the Turkish nation as a people.
Isreal is very wise in how they operate, they understand they need to keep their enemies divided and know who to support and when to attack. For example they don't make mistakes like erdogan made in syria where he made everyone in the region his enemy all at the same time. Isreal has friends until she picks off enough of her enemies and then those friends all become her enemies.
As Isreal has grown in strength and her regional arab neighbours have become weaker and totally ineffective, she has upped her support for the PKK project feeling now is the time to go all in with them.
It also doesnt help that Turkey has grown in military might and population, the TRNC is also a great strategic threat to Isreal. It potentially allows Turkey to project power directly into Isreal in case of any conflicts.
Unfortunately i don't see isreal changing course, they understand that to survive everyone else around them has to fall down. The fact they keep incrementally working to wipe out their palastinian population and take away their lands show they are not interested in any peaceful settlements.
And even if Isreal said tomorrow here palastinians have half the land and become a country would the arabs really live in peace with Isreal? I don't think they would. So you have a situation where its natural conclusion is going to be "survival of fittest"
The arab states don't even want to live in peace with Turkey, its impossible that they will ever live in peace with Isreal.