Are my mother's prayers that she performs in the afternoon considered rawatib or nawafil, and is she sinful for delaying the Dhuhr prayer past the congregational time due to her preoccupation with childcare?

It is permissible to perform the ratibah qabliyyah (sunnah (definition) prayer before the obligatory one) after the faridah (obligatory prayer), and it will be considered a ratibah by intention, even though performing it at its prescribed time is better. A woman is not religiously obligated to offer the Dhuhr prayer before the congregational prayer in the mosque ends; rather, she can pray immediately after the time for it begins, and the Dhuhr time extends until the Asr prayer begins. A woman is not religiously obligated to pray in congregation at the mosque; her prayer at home is better. The mother should not be burdened with raising grandchildren to save on nursery expenses.