All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
If you are inquiring about the validity of the Tawaaf (circumambulation around the Ka’bah) of your wife without her being accompanied by you, then her Tawaaf is valid whether she performed Tawaaf alone or with your mother as it is not a condition for the validity of the Tawaaf of a woman to be accompanied by her Mahram.
In addition to this, the farewell Tawaaf after performing ‘Umrah is a Sunnah according to the view of some jurists and it is an obligation according to some other jurists.
Allaah Knows best.