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If K_1 sqcup K_2 is a split link in S^4, a splitting sphere for K is an S^3 in S^4 such that K_1 lies in one connected component of S^4S^3, and K_2 lies in the other. We show that there exist infinitely many pairwise non-isotopic splitting spheres for two unlinked, unknotted S^2’s in S^4. Along the way, we introduce barbell diffeomorphisms of 4-manifolds, as constructed by Budney-Gabai in their paper “Knotted 3-balls in S^4”.