Hard to tell where your exact issue is without seeing all routing and firewall rules.
But if your USG20W is acting as wireless AP only (no internet connection directly to it) I'd recommend to create the 192.168.2.x network on USG50 and get rid of the NAT (I'm assuming your have on USG20W today since I see your connection to WAN port).
The USG50 will automatically add the required static routes between 1.x and 2.x LANs and all you need to do is appropriate firewall rules. And take care of your WLAN (which seems to be working today based on your description).
Suggested setup on picture below (can be further improved/simplified if you describe what your desired setup is and if the two switches are VLAN capable).
Also 2.x network can be bridged with 10.59.x network to make things even simpler.