#switch help

So I have my mom’s house on my acnh island bc i made her an account on my switch. Due to personal reasons I won’t be getting into here, I don’t want her house on my island anymore, but I also don’t wanna just delete it, I wanna have it in my back pocket in case I wanna restore it, so my question is this;

can anyone explain what's up with the cart on the left?

it was in my switch for a while, but when i restarted my switch for the new update, the game wouldn't run. I tested whether or not it was a problem with the switch itself by putting a different game cartridge in (the one on the right), and it read it just fine.

Weird.

If I shake my system the motion controls toggle on for a split second and causes the camera to go up and down and shift around for a split second.

also somehow one of my controllers disconnected?? it turned off????

I bought animal crossing (the cartridge) and my switch is saying I need to “download the game.” Apparently in order to download it, I need to be connected to the internet (which is the part I don’t understand, because I bought the cartridge version and didn’t buy from the eshop). Also, my switch has NEVER connected to the internet, but I did uninstall/delete the game after I played for a bit because I wanted peaches but had pears, so I thought I’d just restart.