I don't think the room or what you've done with it is as big a disaster as you've made it out to be.

I would not do built-ins. The room is already long and skinny; adding built-in on a long wall is just going to make it skinnier. Don't shiplap. Besides being overdone, I don't think it works with the brick fireplace.

Sectionals are not ideal in small living rooms or rooms with lots of constraints limiting furniture placement. But you don't have really a lot of constraints other than the fireplace, and you've said you want the table there anyway. Since your windows are high up, you actually have three walls where the sectional would fit easily, though it makes sense for TV viewing to put it on one of the long walls.

I'd probably put the layout much like you have it, maybe adding a chair to the conversations group on the fireplace side. I'd probably change out the rug. Maybe work on the lighting. It's hard to judge from a photograph, but the light level seems low and the whole room has a yellowish cast that could be fixed by changing the color temperature of the light bulbs (or it could just be the photograph). If the lighting changes don't do the trick, I'd think about a different paint color.

But honestly, I don't think I'm getting what you think is so terrible about the room now. Everything I just wrote is pretty minor and based on MY preferences and may not apply to you.

I resisted scrolling down to the picture before reading your whole post. Talk about disappointment. Where's the little room of horrors?! :)

I agree with cawaps. I would not do built-ins and I'd look into the lighting situation. Tell me about your table though. It's hard to judge from a photograph but it looks smaller than 42". I'm wondering if you need a larger table to sit four people around. Also, when you say you eat in this room, do you mean at the table or sitting on the couch while watching TV? If the latter, perhaps tray tables would be practical.

The school supplies. Did I understand you homeschool? Do you need closed storage under the TV that could hold games and school supplies?

Were you planning on replacing the two red chairs? What's in that area of the room? Are you feeling overwhelmed because the room needs to be a little bit too multifunctional?

Hmm. I think I might build in a homework station with two seats under the window where those two red chairs are currently. And then I think I'd swap out your round table for a small rectangular one with the short end facing the FP. Find a new home for the keyboard/kid chairs and shift all the furniture/TV down toward the other window wall. The round table you currently have the table lamp on looks like it might be too big for the space.

Also, I'd seriously consider getting some better recessed dimmable lighting in that room. Could be your photos, but it feels very dark in there.

For display shelves, I'd probably have bookshelves flanking the window. Putting them on the end will visually shorten the long room, which is a good thing. I'd probably put a media console under the TV, maybe a bit longer than what you have now.