How do you explain the sentences like 집에 데려다주십시오 or 옷을 가져다주십시오? Don't we say 데려주십시오 or 가져주십시오?
Your second example is easier to explain in a logical way:
Because 가지다 can mean 'carry' or 'keep', this could mean 'carry the clothes for me', or it could mean 'you keep the clothes'.
This is short for 옷을 가져다가 주십시오, and it is clearer because it refers to two specific actions - carry the clothes and (then) give them to me. So it's a clearer way of saying 'bring me the clothes'.
It's not really so clear that there are two actions taking place. It's easier to think that this is just the accepted idiomatic way of saying 'please take me home'.