Is expiation incumbent upon someone who did not adhere to reciting Surat Ya-Sin and Surat Ad-Dukhan for his mother weekly, based on her will, knowing that he did not withhold from her ‘Umrah and supplication?

It is permissible to read the Quran and dedicate its reward to the deceased according to the majority of scholars, and this is the preferred view. There is no sin upon you for not reciting what your mother asked for, and there is no evidence for the specific virtue of reciting Surah (definition) Yasin and Surah Ad-Dukhan at a particular time. Persisting in such an act may fall under the category of an added innovation (bid'ah idafiyyah). It is recommended to strive in supplicating for your mother and giving charity on her behalf. It is permissible to dedicate the reward of reading the Quran to her.