To expand on this: Is there any other way to return a province to a country or even my vassal that would increase our relationship? In order to vassalize Savoy as france I firs that to take Savoie and Nice to bring the vassalization cost below 100%, after I vassalize I'd like to return those provinces to save the AMP for coring...
If you do Return Core in a peace deal, then that boosts the relationship.
So Switzerland holds some Savoyard cores. You DOW Switzerland, get high WS, then in the Peace you force them to Return Cores on some provinces, to Savoy.
Relations with Savoy will be boosted by +40 for Returned Core To Me - per province, with no maximum.
Note that there's also another modifier, Liberated Our Province, +25. But to get that I think it needs to be currently sieged by an active war enemy, then you siege it back for them in that war. So you need to be at war with an ally or vassal, and have the enemy siege one of that ally/vassal's provinces which you then siege back before the war ends. I don't think it comes from the Peace.
Finally there's +10, Gave Province In Peace; I'm pretty sure you don't get that as well as Returned Core, I think that's when you give a non-core province to an ally in peace.
Here's further details on all the "At war with" modifiers available:
How to boost relations with subject: via war.
And here's a table that summarises them all:
Summary of subject nation relations modifiers obtainable via war.
(Note that the modifiers listed are not unique to subject nations. But unlike many other relations modifiers, they do work with subject nations, and hence are of particular interest one when is looking for the +190 to integrate a heretic vassal/PU)
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