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.
Tawaaf Al-Ifaadhah is one of the pillars of Hajj, and the beginning of its time according to the Hanbali and Shaafi’i Schools of jurisprudence is after midnight preceding the day of Al-Adh’ha, and according to the Maaliki and Hanafi Schools of jurisprudence, it begins at the second Fajr of the day of Al-Adh’ha, therefore, it was not acceptable from you to perform Tawaaf Al-Ifaadhah before that.
If you doubt whether or not you had performed Tawaaf Al-Ifaadhah, then you are obligated to perform it; Al-Maawirdi said in his ‘Al-Haawi’: “The Tawaaf and Sa’y are among the pillars of Hajj, and whoever doubts whether or not he had performed any of the pillars of his Hajj, he is obligated to perform them, it is like the one who doubts about one of the pillars of the prayer, he is obligated to perform it….”
However, if you had performed Tawaaf Al-Wadaa’ (Farewell Tawaaf), then this Tawaaf replaces Tawaaf Al-Ifaadhah according to the view of the majority of the scholars whereas the view of the Hanbali School is that it does not replaces Tawaaf Al-Ifaadhah; rather, one should make Tawaaf Al-Ifaadhah while having the intention to perform it. The Fiqh Encyclopedia reads: “The view of the Hanafi, Maaliki and Shaafi’i Schools of jurisprudence is that if someone performs a correct Tawaaf after ‘Arafah – whether this is an obligatory Tawaaf or a supererogatory one – it replaces Tawaaf Al-Ifaadhah even if he did not intend it…But if someone did not perform Tawaaf after ‘Arafah and went back to his country, then he is obligated to come back while assuming the state of Ihraam so that he would perform Tawaaf Al-Ifaadhah, and he remains in the state of Ihraam in regard to women [i.e. he must refrain from having sexual intercourse with his wife] until he performs a valid Tawaaf. As regards the view of the Hanbali School of jurisprudence, if someone did not perform Tawaaf Al-Ifaadhah but he performed Tawaaf Al-Wadaa’, or a supererogatory Tawaaf, then the Tawaaf which he had intended will count and it does not replace Tawaaf Al-Ifaadhah. Even if he returns to his country after this Tawaaf, he is obligated to return to Makkah while in a state of Ihraam so that he would perform Tawaaf Al-Ifaadhah because it is a pillar [of Hajj], and he also remains in the state of Ihraam in regard to women.”
To sum up, based on the opinion of the majority of the scholars – which is the correct opinion Allaah willing – your Hajj is correct and you may now perform Hajj on behalf of your mother.
Allaah Knows best.