I'd suspect that the tablet is sending garbage to the router when it's charging, but replacing the tablet would be
a lot cheaper than having a lab figuring out what the tablet is doing. (They'd have to run a pretty good recording spectrum analyzer on the tablet, then analyze the recording. Something like that would run into the thousands of dollars.)
Back up everything on the tablet (see
Backing up an Android Device if you don't know how) then reflash the ROM (see
[Samsung] How to flash Stock ROM via ODIN) and see if that helps. If it doesn't, you have a hardware problem, and replacing the motherboard (which would be the first step) probably wouldn't be worth the price. (You can buy a new one for about the same price.)