Gaming over wifi is not ideal, but if you're seeing ping over 1000ms then that's very unlikely to be the fault of the wifi. Do a few speedtests from a PC or Mac connected to the hub by a network cable, particularly at peak hours and see if you're consistently getting the full contracted speed, because poor latency ("ping" to the masses) is often associated with speed problems.
Also, a job for your son if he's old enough, get him to visit thinkbroadband.com create an account and then set up a Broadband Quality Monitor. That will continuously monitor the quality of your cable connection although it will need to run for 24 hours before there's any useful data. Then post a link to a snapshot chart of your BQM in a reply here, and we'll take a look.
The BQM is run by Thinkbroadband's servers, there's nothing installed on any of your devices, and it can be checked by logging in to your Thinkbroadband account from any internet device anywhere (so for example, I keep an eye on an elderly relatives Openreach line through a BQM set for their IP address as well as one for my own), there's nothing installed on either my computer or theirs. And because the BQM is simply sending a ping request to your router, you can happily turn off other equipment if that's how you normally behave - only the router needs to be switched on.
Good idea to test the lag with a cable, but be aware that lag problems tend to be high unpredictable, so you may want to try that for a day or two if that's possible.