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 Yb3(OH)7SO4·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 Yb3(OH)7SO4·H2O is elucidated by comparison to the lutetium analogue, Lu3(OH)7SO4·H2O. The degree of disorder in Yb3(OH)7SO4·H2O is controlled by the chemical form of the starting material and solution pH. In a low magnetic field, Yb3(OH)7SO4·H2O displays QSL behavior, while, under a high field, a valence bond glass state is observed. The degree of stacking fault disorder in Yb3(OH)7SO4·H2O modulates the observed magnetic properties and the transition between QSL and valence bond glass states.