The forms of nōs and vōs exhibit a pattern, except in the genitive (nostrī/um, vestrī/um) and the possessive (noster, vester). Did vōs originally resemble nōs in all its forms, only to diverge later? If so, what caused the change, and why did nōs remain the same while vōs changed (or vice versa)?
Yes, the forms of vōs did originally resemble those of nōs. But there was a sound change in Latin whereby the sequence vo became ve; this is an example of dissimilation. Apparently this only occurred when the o was short, which is why it did not happen in the word vōs itself. Other examples are adversum, veto, which were originally advorsum, voto.
Weiss (Historical and Comparative Grammar of Latin, p. 140) states that this change only took place when ve was followed by a dental, and that, based on inscriptional evidence, it occurred in the second century BC.