Would anyone have an opinion what would be safer, to have a Remote Desktop Port open on the Firewall and Router (with a strong pasword for logging in to the desktop) or the Router SET to accept remote control (with a strong password) with the idea that I would log into the router and enable and DISABLE the router rule ALLOWING for incoming RD port, as required for doing remote desktops. So router blocks RD when I am not using it but the trade off is that my router is always listening. Router is a Netgear.

Open router or open RD?Neither; use VPN, preferably IPSEC.  Does your router have any kind of VPN support?Yes, it is a "Neatgear ProSafe VPN Firewall FVS318v3" Now what?That's good news.  Read the manual about setting up VPN on the router; it will probably also provide instructions on setting up the client machines (the remote computers that "dial in" using VPN).

Every router's setup is slightly different, HENCE why we have to SEND you to the manual first, but let us know if you get stuck.