It depends on what you hope to gain from the information to be gathered. Investigators are expensive and they will expect to be paid whether their reports are helpful or not. The decision should be made by weighing the cost against the potential benefit.
If you do hire an investigator, keep it to yourself. The advantage of securing information without the other party’s knowledge lies in how that information is utilized. The premature release of the information will allow a dishonest person an opportunity to manufacture an explanation or excuse. On the other hand, if the dishonest person believes he/she is safe in misrepresenting the facts (i.e., lying during a hearing or in response to discovery requests), then the impact of the information can be devastating. It is important to give the other party an opportunity to choose between truth and prevarication, then you can decide what action should be taken.