Looks like your straddling rustic country, oriental and comfy middle American style. What do you consider modern? I see you have an ideabook. so I'm picking my favorite look for you from what you've uploaded there. T https://www.houzz.com/photos/avenue-road-condominium-contemporary-family-room-toronto-phvw-vp~74063

I would love for it to look something like this...

Honestly I just want rid of the pine/oak color that reigns the house. I want to get rid of any Country/Cabin feel in the house. I already want to paint all the doors white and get new darker flooring.

Have you checked on bleaching your current floors &/or ceiling to look more like the photo on the left?

My floors are vinyl. The ceiling is real wood, so I don't want to do anything to it. I just wanna leave it alone.

Dark but warm flooring that won't fight with the warm ceiling would be the way to go.

Resurface the hearth, get a modern wood stove, buy modern furniture. Also, get rid of the verticals. Any house can be made to look modern regardless of the wood floors etc. modern furniture will do wonders for your space. Check out Room and Board for examples. Your house appears to have a great flow that is perfect for a modern design. Good luck!

You've got all the elements of modern in your room already. Just a few tweaks and you're there. I echo the idea of replacing the stove with a more contemporary shape (think spaceship) in white and getting rid of the rock hearth. If needed you could create a surround in a matte white tile.
Replace the ceiling fan with a Sputnik inspired fixture in chrome and glass and all you need to do is update your furniture to something sleek and modern. You've got the room for a sectional and I'd add a rustic cocktail table with glass to pull in a California modern feel.