For the living room rug, I would go for something like this:

http://www.overstock.com/Home-Garden/Handmade-Flat-weave-Stripe-pattern-Gray-Black-Accent-Rug-2-x-3/8184405/product.html?refccid=7WNVV6COS2K3Q72ED5TOWT4YSI&searchidx=26

or

http://www.overstock.com/Home-Garden/Alise-Metropolis-Area-Rug-710-x-103/8066342/product.html?refccid=5Y56XOHJ6T4L74KEJVAZR37TJQ&searchidx=197

For the dinning chair covers, I would pick up one of the accent colors either from the two green chairs or the pillows that are on the chairs. Not sure how adventurous you are, but I think that either a pattern or a solid green or pink would looks great in your space.

I like the patterned dinning chair and it goes well with your green chairs in the living room. In that case, I would go with the patterned dining chairs and get a red or pink rug to accent the red/pink hints in the art piece in the kitchen, dining chairs and pillows on the living room chairs (I actually like the white pillows you have).

Something like this may work:

http://www.overstock.com/Home-Garden/Nourison-Vista-Floral-Paisley-Multi-Color-Rug/7547224/product.html?searchidx=2

or

http://www.westelm.com/products/distressed-arabesque-wool-rug-shockwave-t1805/?pkey=cpattern-rugs-flooring||

Diane,
it can be tricky when you have a space that multitasks as yours does; luckily
you have a beautiful space to work with!

With
the different functions of your great room and children who play on the floor,
we agree that a heathered effect would be a wise choice. You may want
to check out the Caress Collection, Shaw’s softest, dig-your-toes-into-it
carpet – specifically Angora IV or Devon IV. If your kids especially enjoy lying on the floor,
a Caress bound carpet will be up their alley. And since it’s stain-resistant,
it will be up your alley, too. You can bound any Caress carpet into a
custom-sized rug, and the styles we shared also come in different levels so you
can find what matches your price and plushness.

Best
of luck with the great room and new home!