Do you need further surgery if part of the root of the Basal Cell Carcinoma was not totally removed?

Removing residual basal cell carcinoma is not always easy. Because the projections(roots) are microscopic in size, they can't be seen with the naked eye. Even utilizing Mohs surgery, which traces those projections or roots, may fail if the tumor that is still present can't be detected. However, if Mohs surgery is used and the removal can be made below the level of the previous surgery, the chances are much greater that the residual tumor could be removed. Identifying this level is not always easy either. A fellowship-trained Mohs surgeon would be best equipped to do this provided enough information about the first surgery was made available.

It depends a little on the pathology and the site of surgery. Certainly if the pathology shows aggressive features MOHS surgery would be recommended. Deep margin incomplete excision is a concern and much more of a concern than incomplete excision at the superficial margin. Maybe clarify where the incomplete margin was - if as you state it was the deep margin - I would personally re-excise if this was  reconstructable. The other option is radiotherapy.

If your mother is not elderly and is in relatively good health  I think it is a good  idea to have the rest of the basal cell removed .  Otherwise it will just grow back  and make removal more difficult in the future . It could also be more disfiguring .