SPOILERS
In the last chapters of the main story in the novel, yes they do fight over Nain. Though they compromised and tolerated each other for Nain's sake because of what happened to him (another spoiler)
In the special chapters, Amon and Gwen do not really interact with each other except on special occasions as Nain avoided for them to cross paths. And yes, they do have their own schedule on interacting with Nain.
ps. sorry, english is not my first language so pardon my grammar

After reading about the spoilers on their love triangle, I'm so curious on how Gwen and Amon interact. Do they fight over Nain? Do they fight for his attention?? Do they interact with Nain at same time or do they have their own schedule???
Spare changggeee