mirroring my project

Hi

I really don't know where to start or even if this is the right group,
but I must start somewhere.

I wrote a c++ code which uses a library provided by a commercial
company XYZ co. as an api to connect to their server, the code also uses
other open source c++ libraries.

The code must stay connected to XYZ, so I keep my PC "linux" running all the
time, but when the power or the internet connection is down, so is my
connection with XYZ which is the problem I need to over come.

can I mirror my PC setup and place the mirror set-up on a server
somewhere else in the world "possibly closer to XYZ server" and have
the mirror and the PC at home talk to each other to make sure one of
them is connected and doing whats suppose to be done, if not then the
other kicks in and the first waits in case the second fails and on we
go?

if so, how can I start, any terms to search for, any links, I need the
big picture and the details in order to pull this together.

many thanks