Is an expiatory oath (kaffarat yameen) or anything of the sort incumbent upon the mother if she swore not to give her daughter a device for a week, contingent upon the performance of a specific act, and then the daughter took the device without her mother's knowledge before the period ended?

You should have obeyed your mother and repented to Allah for your disobedience to her.

If your mother did not give you the device, there is no expiation upon her unless she intended to prevent you from it. Intention affects the oath, and if she intended to prevent you absolutely from benefiting from it, then her intention carried a broader meaning than her words.

If she had no intention, and we refer to the reason for the oath, which was to prevent you from enjoying playing with it, then by your taking it, you have broken the oath, and expiation for an oath is due upon her.

You must inform her of this.