Protein "A" must be co-expressed as it does not express well alone.
Have you tried separating A+B on the Nickel column by flowing 2M urea to help "tickle" off protein B. The amount will vary depending on the affinity. In my case (~50nM) requires about 1000-1700ml of 20mM Tris, 2M urea pH 7.5. Then you can add unlabelled purified protein B to labelled protein A. Dan