Since it sounds like you have a wired connection on the third floor of the house, the best solution is to use a wireless system based on a centralized controller where all the access points are managed as a single entity. There are two different types of this system: one with an actual physical wireless controller and another based on a virtual wireless controller. The latter is what I would recommend for your uses. Some manufacturers of this type of equipment are Ubiquiti, Cisco/Meraki, or Aruba Networks. Meraki uses a cloud based system while Aruba uses software in the APs which form a peer to peer network with other APs and one of the APs is set as the master to control the entire network.
Another solution is to use a solution such as SonicWall which will replace your router/firewall. All the SonicWall firewalls have built in capability to run as a wireless controller. You just purchase the SonicPoint APs and connect them up to the firewall. The firewall will then manage all attached APs.
The less optimal option is to use another wireless router or a stand alone AP and connect it up on the third floor. You will need to configure this device to use the same SSID but on a different channel from the current wireless router you have. In the case of using a wireless router as an AP, you have to shut off the DHCP server built into the router.
Another solution is to use a solution such as SonicWall which will replace your router/firewall. All the SonicWall firewalls have built in capability to run as a wireless controller. You just purchase the SonicPoint APs and connect them up to the firewall. The firewall will then manage all attached APs.
The less optimal option is to use another wireless router or a stand alone AP and connect it up on the third floor. You will need to configure this device to use the same SSID but on a different channel from the current wireless router you have. In the case of using a wireless router as an AP, you have to shut off the DHCP server built into the router.