I would use the space off the kitchen like a family room with the T.V there . The other space like a nice LR for adult conversation and why would you want a brown sofa when there is already so much brown in the space.With 2 kids I would be looking at getting rid of the carpet and getting wood floors and I for sure would not have T.V. in both spaces. I hate TV in my LR use that nice big space for some seating , not a sectional, that is conducive conversationand I would probably add a fireplace in that large space for a focal point.

The circulation pattern has been set by the architecture and unless people fly over the area there is no way to keep people from walking in front of the TV, however, this happens in the majority of homes and people adapt.

Your seating area needs to join your fireplace. Larger rug, orientate the furniture so you have a cozy space in front of the fire. The run around/games/play area I would have behind the couch I would use as a room divider of sorts. A proper games table could one day set where the coffee table is now. While shutters are very private they will never give a room the softness, warmth, color of proper curtain panels. I would add a panel where the verticals stack to hide them away.

Update: we worked with houzz://user/callmaeday. She was fabulous. We realized in talking with her that we really needed a different couch. Luckily we were able to return the one we originally purchased and get one that fits out needs better. The layout with the couch in the middle of the room is actually what works best. Now I just need to find the time to get end tables and a console and pictures and all the other stuff to complete the room and make it feel like home. I’ll post pictures when I have the final. You all were very helpful. Thank you! I would have never ended up with this layout without all your suggestions