Depending on your current devices, upgrading to a better Wi-Fi access point would probably be a better solution in my opinion.
So if I understand this correctly, my simplest solution would be to buy a switch to gain more router ports, then run an Ethernet cable from the switch to a Wi-Fi access Point device out on the back deck.
There is no point in my asking for recommendations of what switch and what access point device to buy, because I will be limited to whatever my local computer supply store has on the shelves. High performance (bandwidth and speed) are not a priority here, the nearly exclusive use will be for my wife to look at cat pictures on Facebook.

Do I kind of have the idea? (I told you I know next to nothing about networking and Wi-Fi, it's all black magic to me.)
tanstaafl.