Assuming the NAT type is one that supports peer to peer connectivity, you could try using Ethernet instead of wireless (of course this only helps when docked). This would alleviate issues with WiFi signal not being strong enough, potentially increase bandwidth, and reduce latency. Ethernet can’t improve the connection beyond the incoming connection from the ISP, it only will improve issues that stem from wireless connectivity.

I live in the countryside with my family, so maybe that’s why my Internet is so wonky?

it could very well be this, when I visit my parents in the countryside the internet is sometimes not good enough, and other times it is adequate (satellite internet, so weather can impact it).

At least on the Wii the ATI logo isn’t a sticker, its actually physically on the plastic shell similar to the wii logo on the front

I sadlt can’t tell you if its printed, laser etching or some other technique