I pulled pixels from your kitchen photo to get the colors you are keeping from the wall color, flooring and countertop. They are represented by the three swatch columns to the right of the chart below.
I then substracted some color saturation from the lime green to come up with a hue I think might work well on the cabinets with some new hardware---perhaps a bright polished copper color. As you can see it is a rather nice blue-green.
Note that although you were not planning to change the kitchen wall color, I think it would add a lot to paint the "soffit" above the cabinets a lighter value of the same color. Right now, I find it too intense. The new value range for the top of the wall is on the far left.
Obviously I am guessing on transition to coral in the other room. I would be happy to play some more if you have other ideas or can share a pic of that coral color.
If you like the hues and values shown, use a pixel grabber to get the RGB color code of any. Then go to www.easyrgb.com
(a free site), pick a major paint manufacturer a paint color collection, enter the RGB codes, and the system will kick out the names and numbers of the four closest paint chips.
Then as Joe suggests, you can use the paint company's free visualizer to paint your room virtually if you want. The visualizers are free but you may have to use the version you download to your machine in order to mask off and save your own photo. No big deal. For the Benjamin Moore program you also have to download Adobe Air but it is free too.