Am I obligated to offer expiation for an oath (kaffarat yameen) after I vowed not to see my wife and children for the first three consecutive days following their return from travel, and their return has indeed occurred?

The vow not to see the children for three days is not an act of devotional vow (nadhr qurbah) that is obligatory to fulfill. Its purpose is to be a permissible vow, and there is a difference of opinion regarding its validity. Therefore, there is no harm in seeing the children and not fulfilling the vow. At most, some jurists consider it to necessitate an expiation for breaking an oath (kaffarat yamin), while the majority of scholars believe nothing is obligatory. However, if one offers expiation as a precaution, it is good.