In indian context, mediation and counselling are synonymous and interchangeable. Go to the literal meaning, mediation is a process, where both parties sit together and with the assistance of mediator (who can also say the legal consequences of actions the parties want to take) resolve their problems. In counselling, the counsellor by talking the parties together and individually find out the origin of problem and give a definite solution to the problem. If the affected party accepts such a solution, then co-habitation can be achieved. Generally, in counselling, the psychologist's counselling will help the parties to resolve their problems.
If the matrimonial dispute is not concerned with dowry, most of them can definitely be resolved by the able assistance of expert psychologists. But in our mediation centres, we have been engaging the experienced advocates and some times judges/ retired judges, who can think legally and try to show worldly knowledge without understanding the root of the problem.
The inlaws' general complaint about DIL that she is lazy, spendthrift, not respectful to elders, controls husband, does not prepare food properly etc. etc. are basically related to psychological problems and can be solved with the able assistance of psychologist. Similarly, DIL's complaints against inlaws that they control the husband, not allow him to spend time with her, always use her as cook, insult her parents on one pretext or other etc. are also psychological problems. Even extra-marital relationship of husband (even though it is a fact), espousal's suspision about other's adultry are also psycholigical problem. Most of the husband's complaints against wife and vice-versa are psychological problems. In a nutshell, most of the problems are psychological and can be solved by psychologists instead of courts. But, we do not have such facility to have an expert psychologist to assist the estranged parties in the counselling centres.
Finally, to your querry, you put your opinion very clearly before the judge by writing the application that the matrimonial differences with your husband can be resolved by the assistance of expert psychologist so that the matter be referred to him. If you have any expert psychologist in your mind, you mention even his name also in the application. Otherwise court can send both the parties to the psychologist in its panel or govt. hospital to resolve the problem. Just mediation comprising of expert mediators with legal knowledge cannot resolve the matrimonial problem and they solve it with such immaturity by deciding the quantity of compensation and permanent alimony if divorce decree will be taken by the parties. If they fail in mediation, they refer to the matter to the court for compulsory adjudication.