We would need to see more of your kitchen space to say what would work for floors.

I am redoing this part though so I am focusing on floors

Yes. Grandchildren and irresponsible adults

I haven't heard back

It looks like there are lots of tile, but I have seen some great tile painting out there with patterns or just color.

Maybe just try an area like by the sink where a rug might be to see if you like it and how it wears.

Or lay a vinyl plank tile look (I wouldn’t do a wood look next to your wood floor) on top of the tile. There are some nice ones out there now and would wear well with the pool.

We have tile in our kitchen to pantry to laundry to back door also and its nice not to have to worry about damaging our wood floors there. Your tile goes well with your countertop and cabinets but light colors are hard to keep clean looking. That 12 x 24 you have in your pictures are a more modern size but the blue in them wouldn't look good with your countertop IMHO. If you went dark like the veins in your granite you would have the same problem of showing dirt.

You also have a peachy terra cotta color in your countertops. Would that be a color you would consider? We brought home a lot of tile to see in the space before we could decide because they always look different in your house than in the store. You can get very reasonably priced tile and if not up to installing them demoing the old tiles would save a lot on the cost.