[dba-SQLServer] Remote ETL

Lately I've begun work on a project which involves migration from an
inadequate solution to a much more beautiful solution. Both solutions are
web-UI. I need to migrate a bunch of data from the old system to the new
system. In neither case do I have access using trusty tools such as SSMS.

I think that I have worked around this by a) exporting the data from the
old system to CSV files, then inhaling them into a new SQL database on my
home machine. But although I've dipped into the docs about remote servers,
etc., I have never actually had the need to do this. So I have a few
questions....

Is it possible that from my home, I can set up remote connections to both
the old and the new systems? If so, what info about these instances will I
need to set up the connections? So far I have logins to both but no
apparent access to their SSMS installations, so my hands are somewhat tied
with respect to this setup.

Assuming that both vendors would be willing to supply the info required for
a direct connection (i.e. I run SSMS from home and connect to both
databases, each of which resides in a far-off place), is this possible? So
actually there would be three objects: databases A and B, and my home
machine running SSMS+SSIS, so I can inspect and compare the db structures
in both places and write an ETL package that transports data from A to B.

I've done this sort of thing locally (in my home) but never yet to two
remote instances.

Any advice, guidance, pointers to tutorials, etc. shall be gratefully
received.

-- 
Arthur