The Pro 3 only connects to a hub, not your WiFi. The doorbell and floodlight can connect via WiFi. It would seem that if your problems are with the doorbell and floodlight, use of WiFi could help (no guarantee since it depends on your environment). At least that way you could position the hub for the Pro 3 cameras to be more optimal. Try moving the hub away from your router (or satellite) and check for other 2,4GHz wireless devices that could be interfering with the signal between the hub and cameras.
The router itself (almost) always has more than one Ethernet port. The typical scenario is to have one set off by itself for the modem<>router connection and then 4 more for connecting other devices. If yours only has that one to connect to the modem, use a WiFi extender. That will connect to your WiFi and will also have an Ethernet port for the base or hub to connect to.