Does a mother's giving juice to her daughter, after I swore not to give it to her, constitute breaking my oath?

An oath is based on the intention of the swearer. If your intention was that the girl would not taste the juice that you had prepared, then the oath is broken. However, if your intention was that you would not directly give her the juice, then you do not break the oath. In the case of breaking an oath sworn by Allah's name, an expiation for the oath is required.