It is permissible and there are no specific conditions. Yes, respecting the wife if she is a Sayyida is emphasized by the sharia as it is guarding the noble offspring of the Messenger of Allah (peace be upon him and his holy progeny).
It is not permissible to shave the beard unless growing it causes harm and hardship. If it causes tolerable discomfort then it must not be shaven. The itchiness that you feel is probably because you are not used to growing it.