The quenched structural disorder in frustrated magnets can lead to apparent quantum spin liquid (QSL) behavior or to a valence bond glass state: the transition between these thermodynamic states has not been demonstrated experimentally. Herein, we report the synthesis of a novel layered rare earth hydroxide Yb-3(OH)(7)SO4 center dot H2O as single crystals. The interplay between the strong distortion of the triangular lattice and low point group symmetry of the three distinct Yb3+ sites leads to quenched disorder. The variable stacking disorder in Yb-3(OH)(7)SO4 center dot H2O is elucidated by comparison to the lutetium analogue, Lu-3(OH)(7)SO4 center dot H2O. The degree of disorder in Yb-3(OH)(7)SO4 center dot H2O is controlled by the chemical form of the starting material and solution pH. In a low magnetic field, Yb-3(OH)(7)SO4 center dot H2O displays QSL behavior, while, under a high field, a valence bond glass state is observed. The degree of stacking fault disorder in Yb-3(OH)(7)SO4 center dot H2O modulates the observed magnetic properties and the transition between QSL and valence bond glass states.