Which is correct or are they interchangeable - "My son and I have a team approach," or "My son and me have a team approach?"

A friendly wager with a critic rests on the answer.

IT THE FIRST SENTNCE

The first sentence is correct. The second sentence is incorrect; however, it is an idiomatic way of saying that which many native speakers would use.

My son and I

Here's more on me and myself, which covers this point too.