Never correct either of them in front of each other. In laws relationships are generally formal even if 2 people have grown to like each other.
In worst cases try to take the blame on yourself. Since they are connected through you, this helps in reducing the blowout of that situation from either side.
In the end, always try to explain the position to either of them if you feel they are being unreasonable but make sure to do that one on one. Helps in making them understand better and quicker. Ego sometimes plays a lot in these in-laws relationships, so the best way to handle it is to tackle them individually
Lastly, never overly react in favour or against either of them if it has a probability of disrespecting the other.