Wow, what a beautiful large, airy and light space! My whole house could fit in your room but I think larger spaces are more challenging to decorate. I love your large comfy sofa. Would you consider changing the smaller sofa to two big chairs? Perhaps covering it with a warmer fabric to pick up the blues. Is your style more contemporary or traditional? Do you want this room to be rustic and casual? I would paint the walls in a blue to match your love of blue and your pillows and perhaps change out the rug to match. Then pick up the blues in the pillows and perhaps a throw or two for your family to curl up with and to add interest. It looks like you have room for a big, useful wall unit for the computer and desk and some shelves for books and something blue. The windows probably should be open to let in all your light but some panels to match your rug and pillows to warm it up would be great. I'm a big fan of Pottery Barn in my own home and they have nice wall units in several colors. Their rugs are pretty too. Also, you probably want to tie in the new colors to your dining room walls and windows. The fireplace is beautiful. Do you watch TV there or over on the other wall? If you are going to built a TV into your wall unit, maybe a lovely piece of art over the fireplace. Etsy has wonderful art that you can have custom to your size.
Someone on Houzz sent me this picture for my own room and I thought of it for you because it is so warm. I hope you can open it.
http://st.houzz.com/simgs/e5b20cc4021be9ec_7-1070/home-design.jpg

There are a couple of study secretaries that look like bookshelves, suitable in a living room space. Ideal hideaways for school clutter! I would place one on either side of the tv. See examples:


These come in darker wood tones as well. As the children grow and decide to decorate their own rooms, these can be moved into their spaces allowing you to regain control of the family room.

I would pull the corner sofa away from the wall. There is a lot of empty space in the middle of the room.

Wall colour - I like the neutral walls you have now but these blues are light and add interest to the space:

I think for this size of room and the dominant l shape sofa you want to go sturdy, warm and rustic. First things first I would remove the mirror and clutter above the fireplace. Replace the mirror with a large picture of you and your family - try it perhaps in sepia with a wooden frame. Secondly, the way you currently have you the room laid out means that you sit to watch tv ignoring the wonderful asset you have in this room - the fireplace.

I think trying to ignore TV's these days is futile, its what most of us do in these family rooms so for that reason I would move the TV to the front wall either wall mounted or on a rustic wooden base. I would get rid of the second sofa and replace with two leather/two matching fabric armchairs placed where the tv is currently although further forward a smidge. Change the rug for something deeper and richer and get one over the top larger than life low wooden coffee table for the center of the room (make sure it has storage) and get some complimentary side tables and lamps placed in usual places throughout ie. end of sofas, between arm chairs etc.

I would get rid of the cushions, replace with large beige cushions, brown and a couple of burnt orange cushions (this will tie in with the copper fireplace). If you are able I would look to replace the blinds with wooden shutters/roman blinds to your taste/curtains to improve the warmth.

When you've got the fire going, tv on, curtains drawn and all the family on the sofa it could be lovely and warm and cosy.

As a side note, if you wanted somewhere for the kids to work then a side unit like chemayne posted in a darker color could work or even go the whole hog and separate the living room and kitchen with a large bookshelf/desk combo.

Pillow alternatives to bring in the blues and beiges-

If you decide to display artwork I have original abstract paintings available ~ I also offer custom paintings. Let me know if you have any questions.

https://www.etsy.com/shop/gperillo