The Omnilogic HLWLAN antenna is actually a rebranded EnGenius ENS202EXT acting in bridge mode. It's worth noting that Pentair is also using that same device as a WiFi bridge for their new IntelliCenter.
I suspect that all the WiFi settings are actually stored on the ENS202EXT and the automation system is simply modifying them. With the original EnGenius firmware there is a web interface where you can change them directly but I don't know if Hayward/Pentair have disabled that.
@LordDunlow If you cannot connect to your new router, check that it's using WPA2-PSK and not WPA-PSK or WPA-PSK Mixed (also AES encryption required). If not the AP does show but it won't connect.