Inline Mains Switch with microcontroller
• In my design, what approach might I take to split off the the AC power and transform to DC allowing my microcontroller to operate without needing an independent low voltage DC power supply?

A suitable, isolated DC power supply :)

There are other approaches (non-isolated low-voltage supply), but we want to see you here again, so don't go there.

• How do I integrate a relay into my design to switch the mains power from the same mains source?

There are a lot of topics that show how to connect a relay to a microcontroller. But I would suggest that you google for a 'solid state relay' or (same thing) 'optoisolated triac'. If possible, select a version with 'zero crossing switching'.