How do I permanently delete an old wifi-network?

I have a MacBook Air, with macOS Sierra version 10.12.5.

Not long ago my family and I set up a new airport network, with an airport express relay for the back of our apartment. This network works fine, most of the time, but I have noticed our old network still appears in the drop-down network menu. What's more, it seems to be still somewhat functional at times. Now I have searched the internet and found the same old answer involving the advanced settings in the network preferences. I have removed the old network from the list, and so have the other members of my family on their apple devices, yet it still shows up. Is there any way I can just make it not exist anymore? Truly erase it? I'm afraid it might be running interference with our newer network, explaining in part why we frequently have connexion problems.

I would appreciate any kind of answer,

Thanks in advance!