|If it sees the printer on the home PC and not the laptop then...|
Within Remote Desktop Connections on the laptop go to it's Options, Local Resources tab and make sure Printers is selected under Local Devices.
You may simply need to select "Local Color Printer" from within the office printer's Print dialog box's dropdown.
Otherwise, the office PC does not have the needed driver installed for the specific printer online and connected to the laptop.
If the later and you have admin rights on the office PC then install the specific printer's driver on it and it should then it should see it.