Does it make backup server?

[jackop]

I just moved my websites from a shared server to a dedicated server,
but I just changed DNS name servers for the domains and left all the contents on the shared server.
Because my new server is not stable probably due to hacks,
I'm thinking if I can use the shared server in case the dedicated server is down.
My idea is to add 2 DNS's for the shared server to each domain's name server,
so that when the dedicated server is down my websites will be accessible from the shared server.

Is my understanding is right? If no, then what is the right way ?