Simplify is always a good strategy with play rooms. The temptation to cover the walls with artwork and posters can add to the visual clutter. I would suggest a larger area rug to ground the space and create a soft place for playing on the floor. A medium colour with a fleck from other hues in the curtains and upholstery will help hide dirt and lint. I think you could definitely cozy it up with a warm wall colour to unify the space. Lastly, closed storage for the toys goes a long way to creating order from the chaos. You will have a lovely space the children enjoy and you find restful.

The way to get your own eyes on the issue is to start with a general clear out so you can really "see" your kitchen and "keeping" room. Box up and remove all the stuff - tops of cabs, counters, art on walls, fridge and floor clutter, photos, area rugs. Then dig into the cabs and the hutch and remove all the items you only use once or twice a year. Store those away from the kitchen so you gain more room in the cabs for items you regularly use. Is that a radiator on the wall by the TV? I'm thinking the hutch niche would make a great computer area with a built-in desk. Are there any other doors into this room and is this your only living room? What size is the window at the table? Are you up for more than rearranging things? Any construction you can do? Can you take more pix, comment here and attach images?

Agree with Judith too, paint all one colour as back wall. I like the fireplae and wouldn't replace it. That mirror it too big and not very interesting, doesn't do anything for the wall or the fireplace. The gold I suspect clashes with the metal on the surround, bit too new and shiny. I think a great piece of artwork would really set off the fireplace and make it a gorgeous focal point. As the fireplace is very angular I suggest a more organic colourful piece to soften it up a bit. A real painting rather than a print if you can. Keep an eye out at markets, second hand stores ... or even eBay!

Why not look at serving hatches? As they are open you won't need to keep the glass clean and make sense in the Kitchen setting. If you want to close the noise away then you can using the doors and it wouldn't take up too much space.