Is the correct grammar my mother and me or my mother and I?

Well both 'mother and I' and 'mother and me' are correct. It all depends on the context you are using the phrase. The key is to break down the sentence into two using mother and I or mother and me to see which is appropriate. For example, 'Mother and I went to the market' or 'Mother and me went to the market' To test the correctness, you break it into two sentences. 1. Mother went to the market (correct) 2. I went to the market. (correct) 3. Me went to the market. (wrong) That means the right answer is Mother and I went to the market. Another example, John took 'mother and I to the market' or 'John took mother and me to the market'. Using the same rule above, we have, 1. John took mother to the market. (correct) 2. John took I to the market. (wrong) 3. John took me to the market. (correct) So the correct statement in this case is John took mother and me to the market. Hope this helps. Thanks