Trading with the Wii (PBR) does not work. This is confirmed by R4 team. Wireless trading to other game carts of D/P does work.
So are you SURE you have connected to PBR?
Well, technically
on PBR you don't trade Pokemon, only copy them from your DS cart to your trainer character on the Wii. They remain on the DS cart unlike the Slot 2 GBA to Slot 1 transfer where it's a one way, permanent move.
Once they're copied to the Wii you can battle others using the Pokemon you trained on the DS.
Trading Pokemon only ONLY happens between two DS's either
1. DS to DS wireless (nearby each other),
2. DS to DS using WiFi Connection between two players that have traded friend codes or
3. anonymously using the Global Trading Service with WFC.
Why do I know this? I have an an 8 year old Pokemon fanatic in my house, and is the main reason why in addition to his own, I personally own a GBA SP, DS Lite and several Pokemon carts!
striderx