Answer: The function of the noun phrase "My mother and I" is subject.
Step-by-step explanation: The subject is one of the most important parts of a sentence. The subject indicates what or who goes through a process, performs an action or experiences a feeling. Moreover, it is generally placed at the beginning of a sentence and it is usually conformed by a noun, a pronoun or a noun phrase. In the sentence provided, "My mother and I" is the subject because it points out who are the people performing the action (the action of going to see a movie). Furthermore, "my mother and I" is a noun phrase.