"would have had" vs "should have"

Question

Are these two sentences grammatical and equivalent?

1 If I had not taken my phone there, I would have had to go back home, pick it up, and take it there.

2 If I had not taken my phone there, I should have gone back home, picked it up, and taken it there.

Answer 1

Question 1

Are the sentences grammatical?

Answer

Yes, they are.

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Question 2

Are they equivalent?

Answer

No, they are not. Saying what one would do is not the same as saying what one should do.

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Examples

1. I shouldn't eat fatty and sugary foods, but I would do so anyway.
2. I should exercise, but I won't.

Answer 2

The correct one is the first sentence, since "I should have gone" has a meaning of regret.