We demonstrate the extension of coherence between all four two-electron spin ground states of an InAs quantum dot molecule (QDM) via nonlocal suppression of nuclear spin fluctuations in two vertically stacked quantum dots (QDs), while optically addressing only the top QD transitions. Long coherence times are revealed through dark-state spectroscopy as resulting from nuclear spin locking mediated by the exchange interaction between the QDs. Line shape analysis provides the first measurement of the quieting of the Overhauser field distribution correlating with reduced nuclear spin fluctuations.