I'm not a dream interpreter, and I don't know one, but here are my thoughts. People (even small children) do often seem to have a favorite side to sit, stand, or walk next to others. For instance, when I am walking with someone, I generally tend to walk on the left side of them. It seems more comfortable talking as we walk if I look to the right at them. It could be something as simple as that.
As far as the cousin feeling like part of her is gone, since they were so close, I would think that would be very normal.