I am looking for a furnished apartment with 3 or more bedrooms to rent
for 2-3 months for around $1,500 a month.  It must have highly
reliable high speed internet and very good telephone support (ideally,
but not required, provided by a major US carrier).  It must be on the
coast of a spanish or Portugese speaking country. I have two small
children so security and health is a must.  I realize that there is
benefit going through a local realtor so I would also be keenly
interested on recommendations for such a realtor or company.

Also, part of the reason I'm doing this is for my family to learn
Spanish or Portugese so I would need to be able to deal in English for
the rental.

You should check this place out, it is more expensive than what you
are looking for, but if you go on the off season November/December you
can get it a half off.
http://www.mancoraperu.com/index.html
USA: 1-800-346-3108

They speak Spanish and English in Puerto Rico and I expect you could
find such a rental on the west side of the island, even winter.