I'd be inclined to move couch & armchair along wall with large recess if they will both fit. Mount TV onto flat wall opposite. You could have a low unit to house electronics, or use the one you have. Have purpose-built storage cabinet w/shelving built into smaller recess. Some of the shelving portion could be backed w/mirror to help throw light into room. Use the shelves for books, objects of art, photos etc., and the drawers or cabinet below to store things you don't want on show all the time. I also think a large area rug will ground the family room area from dining/kitchen. A neutral one perhaps or you can inject some colour. Large art pieces on wall as mentioned. A largish plant in a raised pot would add some greenery. You may find you need a floor lamp near couch & chair. Regarding the kitchen, I think you might be able to fit a narrow timber sideboard at end of island bench so you have some additional storage there. I say timber because it would warm up the coolness of kitchen. I agree undercabinet lights good idea for additional task lighting. You could either go mirror backsplash or some gorgeous tiles. As there are a several changes you want to achieve in this space, it might help to do it in stages. Storage seems to be a priority (fam rm & kitchen) and rearrangement of furniture & TV. I would tackle this first. Additional decor ie rug, art pieces on wall(s) could be addressed next. Then splashback and some additional lighting if budget allows.

Ok so depending on floor colours and overall look that she is going for I think (if she is really adamant) that the blue could work if you change the Amaro cabinets to a whiter shade - this will give it an overall crisp, oceanside feel with the warmth of the soft walnut. Otherwise I would contrast it more with a mid-tone colour splashback in grey/brown tones. Again this totally depends of her tastes... Here's a photo that you could show her with the blue splashback - granted it is a little deeper than her selection but at least she can see it on a realistic scale and of course the timber/white cabinets are flipped in this one. Hope some of that helps!

We have tiles that do not have a gloss finish. They are Encaustic, or at least I think that is what the style is called.

I think that it will look too busy with the contrasting cabinetwork and the patterned tile on the floor. But then Australian tastes and styles in kitchens tend to be cleaner and more understated than our American cousins. I would keep it simpler, with a plain large format tile to make cleaning easier and to visually expand the space. Your current tile is very busy and probably hides grease splatters very well. Best of luck with your considerations, Dr Retro of Dr Retro House Calls