Couple therapy would be the most appropriate mode of help for your mother and father in law's problems. Be aware that any result from this/any other counselling/talking therapy will only help if the people involved are motivated to take the help. Apparently, your mother in law at the moment does not appear to be motivated, but may develop motivation after attending two or three sessions.
Alternately, though rarely, this suspiciousness could be because of some psychological problem like psychosis
, but from the history given does not appear to be so. But if you want to rule it out, a psychiatrist
would be the best person to see.
On a social note, if there is a family member or relative or friend who can be non judgmental, who both your FIL & MIL trust and value, they may play the role of the mediator.
Hope this helps.