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.
Stop wasting time re-adjusting the pattern. Have several lawn sprinklers, one for each pattern.