Question:
Is one allowed to take a shower or shave on a yahrzeit for a father?
Answer:
Ir is permitted to shave and shower on a parent's yahrzeit (except for the first one which is like an extension of the first year's mourning). The only resrtictions are not to go to a wedding, and not to travel unless needed.
Best wishes
Sources:
Rema Y:D 395-3, 391-3.