I agree with your daughter. Or at least a less busy rug

Yes, buy a solid one the color of the green in the girl friend's favorite. Then train your draperies to hang better--you can find instructions online.

This rug below might be the best choice. Your daughter's vision is limited. BTW your space might require a larger size for your room.

I think a plain one but textured but I never am comfortable mixing too many patterns . The chair seems to be sitting in an odd spot with that recliner there next to it I need to see the whole room. The drapes are dreadful , why all the stuff up above them . Too little information to really advise IMO.

Instead of trying to match the florals, which can be tough, what about something with a subtle geometric pattern?

I’m pretty sure you already have a rug - a brownish color that’s larger - the right size - & it’s under the rugs you’re photoshopping in to show us. I like the ones that @deegw suggests - they have a pattern but not a floral design & so they don’t compete with the pretty chair. I do think there should be blue in the pattern since your furniture pieces & lamp have blues. The lamp color is great. The textured patterned rug will be a nice compromise between what the women in your life are wanting! That’s a win-win for all!

I'm so curious what's behind the recliners. It feels like there's a whole room back there.

pellet stove

I take some issue with the chair placement. Seems a bit too close to the door. Are there only chairs in your living room? It's a bit hard to tell from the photos.

I need pics of the whole space please .Post them here in a comment

I like the darker of your two options with the patterned chair.

Can’t get a sense of the chair’s colors (also consider the other chairs). A solid won’t add much interest and I’d avoid florals. Suggest a textured “look“ and ignore colors below if not suitable.

If you want some pattern, add cushions on the other chairs.

I would pick up on the blue in your chair but in a geometric pattern. I also think the chair seems quite close to the entrance door but cannot suggest an alternative without seeing the entire room.