My mother had an inversion appendectomy 27 years ago. About 2 weeks
ago she had a colonoscopy done and found that her appendix is still
there, however inverted into her colon. The doctors are saying that
they have never seen this before and will not give us any explanation
on why her appendix is still there. Does anybody have any information
on this procedure? Why would her appendix still be there? Should they
be removed?

The surgery your mother had 27 years ago was not a true appendectomy,
but an "appendiceal inversion." This is a procedure that is sometimes
performed in cases of suspected appendicitis when, after opening the
abdomen, the surgeon finds the appendix to be quite normal. Rather
than removing it, he or she inverts the appendix. If your mother's
physicians have never seen this before, it may be because this
procedure is less common these days; studies like the one linked below
have cast doubt upon its safety, since a surgeon cannot always detect
abnormalities just by looking at an appendix.

http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&dopt=Abstract&list_uids=86152239

If the appendix is normal why not leave it alone, why invert it? In
this case she was already opened up. She was pregnant at the time and
they had to do a c-section. They recommended doing a appendectomy
because they said that the appendix usually goes bad after having a
c-section.

Inverting the appendix helps to prevent appendicitis in the future. 

The reason the appendix is often a site of trouble is because it
serves as a little "pocket" in which infection can build. Inversion
essentially turns the "pocket" into a "protrusion" in the colon. As an
analogy, consider this: if you had a problem with lint and debris
building up in the pockets of your trousers, the problem would be
solved if you turned the pockets inside out. It wouldn't be very
fashionable, but it would prevent the pockets from being receptacles.