The Internet and my dlink is in basement....I plug my desktop into a cat5 outlet in my office and printer is plugged into my desktop! I run my iMac and laptop via wifi!
This may help you understand why a splitter will not work. Ethernet Splitter How To
Set your other dlink up in your office in bridge mode config IPv4 using DHCP and either try extend a wireless network or join an existing wireless network reboot it and
then do the same for the printer use DHCP for ip/dns then power down/up.