If the same and is referred to twice then it should be a separate sentence clause requiring use of a comma. Since there is no comma there is no indication the and is the same both times.
Imagine saying “It was just me and dave and dave went driving” instead of “It was just me and dave, and dave went driving.” Yeah, maybe its the same dave, possibly readable, but its wrong.
If the same and is referred to twice then it should be a separate sentence clause requiring use of a comma. Since there is no comma there is no indication the and is the same both times.
Imagine saying “It was just me and dave and dave went driving” instead of “It was just me and dave, and dave went driving.” Yeah, maybe its the same dave, possibly readable, but its wrong.
Because your example sentence uses the word ‘went’ rather than ‘was’, you need a comma because those are two separate I dependent clauses.
You and Dave were together and then Dave leaves you and goes driving by himself… me and Dave, then Dave went.
If you used ‘was’ then those would not be independent clauses and therefore a comma would not be used. It was me and Dave and Dave was driving.
Edit: also, why the downvote, we are having a conversation here ??