Laila - I think it's partly because women are better at social interactions. I believe it's part nature, part nurture for us to facilitate the social aspects of our relationships. (Except for Anna & Penstamen's DILs - they were absent that day and no one gave them the notes.)
I also believe that a big part of the problem when the DS/DH doesn't/can't smooth over the relationship between his W and his M is that he never created an adult relationship with his parents. I know in my DH's case, although he left home, he never forged a new relationship with his parents. They talk and give advice and he says "yeah, yeah, whatever" just like he always did. And really, they seem okay with that, because they just don't want to hear "no". You know the old saying "You give your children roots and wings", well I've always said that the IL's as parents did their children a disservice by not giving them "wings".
So how could DH help our relationship, he could work on his own relationship with his parents. He could start being honest with them. When they call, and they're negative (they always rag on him for not calling enough, not visiting enough, not calling sooner, not calling later, not calling when DD is awake - it's ALWAYS something), he could tell them to please stop and change the subject, instead, he just calls LESS and avoids the situation. When they visit, and they press my buttons, he could intercede in a way that doesn't hurt anyone's feelings. If they say something hurtful or controversial, he could (gently) call them on it. And if MIL doesn't like being called on the carpet and reacts poorly, he can call her on that too. (In this case, I'm thinking about her saying racist or mean things, or swearing, in front of DD.)
Because I've done all of these things to my parents. I personally brought my Dad kicking and screaming into this century. He stopped referring to women as 'broads', he made a big effort to not curse in front of DD, he didn't make racist or sexist comments in front of me (without being called on it). I've introduced my parents to their first lesbians and totally put that prejudice of theirs on its ear.
As for smoothing things over for DH, I've asked them to stop talking about something, because it bothered him. I've told them what he likes, what his favourite foods are, and what treats he would appreciate. I give them gift ideas for him. To some extent, I tried to make sure my Dad couldn't get DH alone (for the first few years), because my Dad was a Character, and could easily be taken the wrong way. Luckily, DH is very easy going.