Dolphin Framerate halves when I turn on frameskip.

[Dimitri]

Frame-skipping usually *won't* give you any noticeable performance improvement, especially if the emulation is bottlenecked by your CPU (which I'm quite confident about, especially given how weak your CPU/APU is for modern emulation).
Even if you tell Dolphin to use frame-skipping, the CPU thread STILL has to emulate the same game code, and STILL will be the bottleneck in your situation (you're lowering the graphics throughput without reducing the cost of emulation).

Is that a notebook or laptop? Those aren't the most ideal for GC/Wii emulation, unlike desktops...