i like your post of Godzilla, Kong and the other titans, they are sooo good!!!, i like the Rodan facts as well, though i don't see any of Kong and Godzilla., i was wondering if you would like to do fact;s for them too, if that's okay with you.
As far as my gijinka AU headcanons, it’s pretty similar to what’s in the film. Kong is a peaceful creature by nature, and would rather be left alone or be with his own kind. He does have a relationship with Mothra, with her acting more as a surrogate mother to him comforting the creatures of earth where she can, and providing a healing light when needed.
But when it comes to this rivalry between Kong and Godzilla, it’s usually Godzilla who initiates the battles. I have a headcanon that after the fight with Ghidorah, Godzilla ended up so riled up over ANYONE stepping out of line, that he acted out a bit rougher than usual. And with Mothra not there to stay his hand, he may have been too harsh with displaying his dominance.
Kong will defend himself and he won’t back down from a fight, or bow to Godzilla’s forceful instigation. But I believe this comes not exactly from Kong being there but from Godzilla just being too amped up...especially after hearing a certain familiar call of an enemy he thought was gone for good. And is just taking out his frustrations on poor Kong.
In the end, they have a mutual respect for each other when Godzilla isn’t in a rage-mode, and as long as they remain in their respective territories, there’s relative calm on planet Earth. For me, I believe Mothra may have made a request in the past that yes, if he must fight Kong he could, but she insisted that Godzilla not actually kill him. To keep balance Godzilla can’t just go around killing other titans because he’s in a bad mood, unless they pose a legitimate threat to the balance of Earth. Mothra’s role as Queen might be to keep the King in check, and preserve that delicate balance.
While Kong is perfectly happy in his own kingdom, and doesn’t normally pick a fight with anyone unless they mess with him or his home. He doesn’t really care to be called King of all the Titans, he just wants to be King in his own home, and perhaps find his family. That’s just a few ideas I got while watching the movie, while trying not to spoil the story.