1. With his help, her cow gave birth to a cute baby.
2. Because of his help, her cow gave birth to a cute baby.
3. _______ his help, her cow gave birth to a cute baby.
[What is the meaning of 'with' in sentence 1? Does #1 mean #2? If not, what is suitable for the blank in #3 to be the same as #1?]
1 is perfect and says that he was there to help his cow with the birthing process -- not that he was needed, but that she knew of his presence and nothing went wrong.
2 is similar, but implies that the cow was having trouble giving birth, and his help was needed.
I'd use something different for #3. I'd write, "He was in the barn when the cow gave birth ... "
Or maybe, "The cow gave birth to a cute baby while he was nearby."