If Rey believes Palpatine will kill her friends, and Kylo Ren destroys her key to finding Palpatine and killing him, it could be enough to warrant her anger.
Basically you’re just changing “Palpatine killed your old family” to “Palpatine will kill your new family”, so if you feel like Rey doesn’t have enough motivation to attack Kylo in that moment, then it is just a problem with the theatrical film.
Sorry to bring this up again, but I think this is exactly it: Rey’s motivation to fight Kylo and the FO and eventually kill Palpatine is all about protecting her new family and her newly found purpose of life:
An insignificant scavenger, abandoned by her insignificant and absolutely uninteresting parents for drinking-money on a (somehow not so insignificant) planet, unexpectedly gets pulled into an adventure (-> beginning of the classic hero’s journey as we know it from Star Wars). Up to that point, she has neither a family, community, belonging nor purpose, but all of a sudden she is in the middle of a galactic-wide conflict (plus, the force is awakening in her). She gets introduced to this world she has only heard of in stories (or learned from through stuffed puppets of rebellion pilots) and connects with it (namely with the “good guys” that is the Resistance). End of the first act (the so called “exposition”)/Ep7.
She then begins to struggle with her role as she gets confronted with the reality of her new world. Her somewhat naïve views of the force, Jedi and Sith, good and evil getting put to a test.
Eventually, the second act (“Complication”; Ep8) is perfectly concluded with this (https://www.youtube.com/watch?v=co3QrHKcV9c) scene: Rey introduces herself to Poe, who answers that he already knows her. She at last is somebody, part of something, finally has a “family”. Something to fight for as well as something to fight against. Credits roll.
Then the third act (Ep9) happens, which is supposed to be the climax, dénouement and ultimately the resolution. The structural tendency of TROS to sort of contradict TLJ, at least in one major point (and that is Rey’s ancestry), is what needs to be addressed: make it clear that Rey is fighting for what she accomplished in the previous movies, and that is an identity of her own that is solely based on her role in this adventure of hers (as sort of an unwritten page) and not on blood and cloned Sithlord-Sons and not on parents she can’t even remember, because what cause should she have to stand up in their names?
Rey’s parents really shouldn’t matter. They sold her for drinking-money, and as far as I’m concerned, they can just as well already have died of liver cirrhosis or something. Somewhere, sometime. Doesn’t matter.