[King Prout]

If our Sun became a Red Dwarf which has been theorized wouldn't Earth fall within it's outermost layers?

iirc, Mars would fall within that radius. Earth would be consumed in the expansion. I don't recall whether the asteroid belt or Jupiter would be outside the star. I'm calling in one who can answer.

[rocksblues]

Earth would be consumed in the expansion

I now remember this part of the theory.

[King Prout]

side note - the sun is expected to become a red giant, not a red dwarf. is there such a thing as a red dwarf (aside from a very short communist)?

[beezdotcom]

The size probably varies according to the assumptions made during the calculations - one hypothesis says that Venus and Earth will be spared (but just barely), Mercury (orbit in dashed line) gets eaten:

[RadioAstronomer]

Here is a really good description of the processes, fuel, and resultant sizes during the life of our sun. :-)

http://astrosun2.astro.cornell.edu/academics/courses//astro201/evol_sun.htm