We observed mixing between two-electron singlet and triplet states in a double quantum dot, caused by interactions with nuclear spins in the host semiconductor. This mixing was suppressed when we applied a small magnetic field or increased the interdot tunnel coupling and thereby the singlet-triplet splitting. Electron transport involving transitions between triplets and singlets in turn polarized the nuclei, resulting in marked bistabilities. We extract from the fluctuating nuclear field a [imitation on the time-averaged spin coherence time T*(2) of 25 nanoseconds. Control of the electron-nuclear interaction will therefore be crucial for the coherent manipulation of individual electron spins.