I have a DNS record with three
A records: the main site, and two backups. However, when clients perform a DNS lookup, they reach a backup site.
How can I change the order of the DNS records in
dot.tk's DNS server?
You're touching on a "feature" of DNS known as DNS Round Robin. It's deliberate. You have no control over the order in which records which satisfy a particular query are provided.
It's crude; but surprisingly effective as a load-balancer.
If, in fact, the "backup" machines should not be touched unless the primary fails, you need to be more sophisticated with your zone files. You could change the TTL (time-to-live period) for the A record to a small number (e.g. 60 seconds) and then set up a script to change that A record via RFC 2136 when you want folks to fail over.
If you have 3 A records coughing up 3 different answers, you are supposed to get rough distribution equally amongst the 3. (one can also assume that M$ DNS will screw this up, but I don't actually know...)
The resource records that exist for a specific combination of name, class and type form what is called a resource record set (RRSet). Just like this term suggests (it being a set) there is no defined order for these records.
Even if you did have the authoritative nameservers for your zone, the only point where you have any actual control, answering with the records in some fixed order of your choosing it's still entirely possible (and actually common) for a resolver server to reorder them before passing the answer on to the client and even if the answer arrives in the desired order to the client host the resolver library can also reorder the result.
Just as an example, look at these queries issued in direct sequence to a caching resolver server:
From what it sounds like you are trying to achieve, I don't think adding multiple