AirPrint utilizes the Bonjour service to discover local 'Airprint' printers. Because Bonjour can 'only' discover local printers it makes it almost impossible to reach outside your local network to discover nearby printers.
The best advice I can give would be to purchase a second network adapter (Ethernet or Wireless) and connect it directly to your 2nd 'MikroTik' router. This would then allow you to have the AirPrint server accessible in both networks. An under $20 fix to a complex solution.
The easiest solution however would be to use your second router as a bridge to your main network. However I am guessing you're avoiding this scenario for some undisclosed reason.