Is a blood sacrifice or an offering required of my mother if she performs Umrah in Dhu al-Qidah, with an unconfirmed intention to perform Hajj, or is her situation like that of a resident of Mecca, such that her Hajj would remain mufrad (single) if she completes it?

If the mother performed Umrah more than once during the months of Hajj and will perform Hajj this year, she has become a mutamatti'ah (one performing Tamattu' Hajj), and the sacrificial offering (hady) for Tamattu' becomes obligatory upon her, even if she did not intend it or did not say, "Labbayka Umratan mutamattian biha ila al-Hajj (Here I am, O Allah, performing Umrah, with which I will perform Hajj)." This is supported by what Ibn Qudamah stated in Al-Mughni: "If a person from outside Makkah (afaqi) performs Umrah outside the months of Hajj, then stays in Makkah, and performs Umrah from Al-Tan'im during the months of Hajj, and then performs Hajj in the same year, he is a mutamatti' and owes a sacrifice (dam). Ahmad explicitly stated this."