Well, I'll try to clarify it a little bit more. (even for me)
Server A (SA) will be with hosting provider A (HPA).
Server B (SB) will be with hosting provider B (HPB).
Each server has the website and the database installed. SA is supposed to be the primary server and SB would just be there as a backup.
First, there should be some sort of process that is updating the database in SB.
So, when, and if, SA goes down, people entering the site should be redirected to SB, that it has, or should have, the database updated, so for visitors this redirection is "transparent".
Our question is if that idea of how it should work can be done through proxys, or load balancers, or just through DNS settings (the domain pointing to several IPs from different servers).