FMS does not print, only clients.
Is VPN an option?
Without VPN you can do this with a mac mini print server at each location running a FMP client that has a looping script to handle the printing. If you are traveling anywhere in the world you can print to the printers from an iPad and it takes only a few seconds and not weird iOS dialogs. To set the printer in the script you need to login from the print server the printer is attached to and add the printer from that machine. The alternative is to let is assume the default printer and then use AppleScript to run a shell script to set the default printer to the desired one.
I suppose technically you could run a client on the database server to print to Printer A.
Some more explanation is at Re: Printing with Star Micronics POS Printers