The dns servers don't have to agree on what the IP for an A record is. So the dns server in europe can direct a user to the europe webserver, and the american dns can take the user to the american website etc.

Just set the A records to be short lived (like 60 seconds). That way if europe goes down people will just see the american website until its fixed.

The issue then is to keep those two webservers, mailservers and maybe database servers synced. If you can do that you have an enterprise load-balanced fail-over system for the price of 2 VPS accounts