Interior french doors.

What do you want to do in this room? Do you need separation?

How about an open shelf room divider? Unless you live in a hot/cold climate and need to have it closed off. https://www.houzz.com/photos/sale-street-residence-contemporary-dining-room-dallas-phvw-vp~6680554

Can we see actual pictures? Is it defined by flooring? I am guessing the windows are defining. Why do you feel it needs doors? A wall of windows/glass with a French door in the middle would lovely if the space is worth seeing from the gathering room. (What ever that is.)

i just use my sunnroom as an extension of my living room even though it does have sliding doors.

I need pictures of the spaces there is no way to get help without them.

The furniture arrangement in the Gathering Room will affect what you do with your sunroom. Might suggest you get that worked out first as the sunroom is more of an ancillary space.