When a personal pronoun is used as a direct object, an indirect object, or the object of a preposition, ordinarily your ear will lead you to the correct pronoun. When an object is compound, however, you may occasionally become confused.
Her mother and her is the direct object of the verb was insulting. Strip away the words her mother and to hear the correct pronoun: was insulting her (not was insulting she).
Her father and me is the object of the preposition for. Strip away the words her father and to test for the correct pronoun: for me (not for I).
When in doubt about the correct pronoun, some writers try to avoid making the choice by using a reflexive pronoun such as myself. Using a reflexive pronoun in such situations is nonstandard.
My cousin and me is the indirect object of the verb gave. For correct uses of myself, see the glossary of usage at the back of the book.