Is one obligated to obey a father who demands the removal of the niqab, especially when it causes psychological distress to his daughter? And is refraining from visiting family to avoid pressure considered a severance of kinship ties?

A woman must cover her face from non-mahram (definition) men. There is no obedience to a creature in disobedience to the Creator. The harassment faced by a woman wearing the niqab is not an excuse to abandon this obligation unless it reaches the point of being beaten or imprisoned. There is no blame in reducing visits to family and relatives to avoid their criticisms about the niqab, and to suffice with phone communication, for averting harm takes precedence over acquiring benefits.