In the External Devices Control Panel, under Set Up Printer, check Network Printer and don't check AirPrint. Click + to add a printer on your Mac and see if it sees the printer on the DiskStation. If it does, install that printer with the appropriate driver on the Mac (same one you use to print to it when hooked directly to your Mac). Printing should work.
If your printer has scanning, go back to the External Devices Control Panel, under Set Up printer, and check Network MFP. See if printing still works and now if scanning works.
Then click Enable AirPrint, and select the printer brand and model. See if the above still work and now if you can see the printer and use it on an iDevice.
DS 1512+ w/3GB, 5 x 3TB Seagate ST3000DM001 8.2TB RAID 6, half files/half Time Machine.
Icy Dock MB559U3S-1SB enclosure w/4TB Hitachi UltraStar via USB 3 for files backup
UVERSE to AirPort Extreme + 2 AirPort Express w/speakers. TRENDnet TV-IP312WN camera
CyberPower CP1500PFCLCD Sine Wave UPS
DSM 4.1-2661 w/SSH + SFTP, VPN Server, Syslog Server, Media Server, Mail Server, Mail Station,
Audio Station, Surveillance Station, Photo Station, Web Station - DS Apps on iPad & iPod Touch.