Let me see if I understand: There are two V4; yours and your cousin's. To start with, the Friends List on your V4 was empty. You connected the two V4 one time. The Friends List on your V4 now is full of entries for your cousin's one V4.
If this my understanding is correct, and it had happened to me, this is what I would do:
(1) perform a full reset on my V4. Press the reset button on the back, and select reset from the download/reset menu that appears on the screen. This will take the V4 back to it's "fresh out-of-box" condition. All data (purchased foods & items, character history, friends, skill points and gotchi points) will be gone. The V4 will start from a fresh egg again. After the egg hatchs, try to connect again. If the problem no longer occurs, done. However if the problem happens again it's defective, so try step 2.
(2) take the defective toy back to the store it was purchased from and get an exchange. If the store doesn't have any more, send an email to Bandai explaining the problem and ask them for a replacement toy.