Is it possible to complete the Hajj rituals for a deceased mother who was unable to perform Tawaf Al-Qudum, Sa'i, and Tawaf Al-Ifadah due to illness, without compromising the son's own Hajj rituals?

Your mother passed away while in a state of ihram (definition) and did not complete the rites of Hajj. The preponderant opinion is that you are not obligated to complete her rituals. If someone completes the rituals of Hajj except for the circumambulation of Ifadah (Tawaf (definition) al-Ifadah) and then dies, Tawaf should not be performed on their behalf. This is based on the statement of Ibn Abbas (may Allah be pleased with him) concerning the man whose camel trampled him, causing his death: the Prophet (peace and blessings of Allah be upon him) commanded that he be washed and shrouded without embalming or covering his head, and he informed that Allah would resurrect him in a state of talbiyah (definition), and he did not command that Tawaf be performed on his behalf. Therefore, you should perform Hajj for yourself if you have not done so before, and you should frequently seek forgiveness and supplicate for your mother.