Hi SchyffS - unfortunately your setup is not optimal at all SchyffS.
Your skimmer should be the 1st filtration outside of your tank. So, I would move it to your overflow outlet from your tank, AND not your return (to the tank) from the sump......
If you can, try and plumb your overflow pipe/plumbing directly into your skimmer....
Then you do not need a pump at all, and you just use the gate-valve to control the water flow INTO the skimmer.
This is IF you can at all.... Otherwise, place your skimmer's water supply pump in your 1st sump compartment, and have the skimmer's outlet water flow back into the 1st or 2nd compartment....