Is there a difference between these two sentences?
#1.I should have done it. (It is my duty to have done it by now)
#2. I should already have done it. (It is my duty to have done it earlier)
And is the 2nd sentence grammatically correct?
It is grammatical subject to the adverb put before the auxiliary verb but before other verbs.. The use of adverb 'already' in the sentence modifies the verb done, in other words it makes the action more forceful.