I'm confused by the comment that the monitoring officer has complained. Presumably because this has been raised as a breach of the code of conduct from someone?
A councillor cannot be employed in a paid role by the council for which he is a member. It is considered a conflict of interest. However, there is nothing to prevent a member of the same family from being employed by the council provided that the councillor declares an interest and does not take part in any discussion or vote in connection with that employee (e.g. salary negotiations, performance discussions etc. etc.). In this instance, if the wife is technically the employee, is paid directly by the council via the PAYE system (i.e. using her HMRC details etc.) then I can't see that this is a problem.
However, there may be staff management issues here with the employee not doing their job and an unofficial substitute undertaking the tasks could have implications from an insurance and risk management perspective, and lead to health and safety and employer liability issues. It is a staff management problem, not a code of conduct matter. Is the councillor doing the cleaning to be helpful or as a fraudulent way of getting paid via his wife?