Rarely is a three way timer switch (if such an animal exists) useful. But a regular timer switch can override a 3 way switch setup to do one of: hold the light on all the time or keep the light off all the time.
When the timer is overriding the 3 way switches, you cannot easily set the 3 way switches so the light does what you want when the timer stops overriding, except if you remember which 3 way swithc positions do what.
When cleaning anything including baby diapers, it is better to sweep off or scrape off as much solid and semisolid material as you can first. (1) Less cleaning fluid or detergent needs to be used, (2) Less of a mushy mess which in turn means that bleaches or disinfectants will be more effective.