You'd have to do a dst-nat to a web server that you control, and from there, based on the hostname, redirect to the desired site.
To do the redirect, with PHP at least, it's as simple as
<?php
if (preg_match('/^([^\n\.]+\.)*website1\.com$/i', $_SERVER['HTTP_HOST'])) {
header('Location: http://website2.com');
}
The most difficult part is matching the requests that should be redirected to the web server in the first place. The easiest (although somewhat error prone and inefficient) way is to use layer7-protocol filter. Something like:
/ip firewall layer7-protocol add="HTTP website1.com" regexp="^\S+ \S+ HTTP\/\d\.\d[^H]+Host: ([^\n\.]+\.)*website1\.com.+\n\n"
Once you have that, adding the dns-nat rule is trivial:
/ip firewall nat add comment="Redirect for website1.com" chain="dstnat" layer7-protocol="HTTP website1.com" time="13h-14h,sun,mon,tue,wed,thu,fri,sat" action="dst-nat" to-addresses="192.168.0.254"
(replace 192.168.0.254 with the IP of your web server)
P.S. The regex in the PHP, and the equivalent portion in the layer7-protocol both ensure you redirect website1.com
as well as all of its subdomains.