Every time I try to talk to Ulfric Stormcloak he always tells me to talk to Galmar because he needs me to run an errand. But... Every time I try and talk to Galmar he always tells me something about Ulfric joining the Empire. They always redirect me to each other! I also can't start the "JAGGED CROWN" quest because this quest is getting in my way! It puts me in a constant loop of nothing! Any help would be appreciated! Thanks.
If you can load an earlier save point - Upon completing the objective in Joining the Stormcloaks, enter the Palace of Kings and proceed to the room where Ulfric and Galmar are debating and instantly talk to Ulfric. It requires multiple attempts of requesting to talk before he finally does but once he talks to you, you will be able to continue the Season Unending quest as normal.
I've had this bug, which it is, too while playing skyrim a couple years ago. I had to reload an older save but it seems they have fixed it so maybe you need to update your game?
Maybe siding with the empire or at least get to the beginning of their jagged crown request will help you out and then try getting the stormcloak quest.(I havent tried this myself)
That should help you out as much as possible and maybe you can add your findings afterwards.