http://revach.net/article.php?id=1830

Section: Halacha   Category: Tshuvos
Rav Moshe Shternbuch: What To Do When You're Helping Mommy, And Daddy Comes Calling
The Halacha is that when your father and mother both need your help you must help your father first because both you and your mother need to honor your father.  What happens, asks Rav Moshe Shternbuch (4:208), if you are already in middle of helping your mother and then your father needs help.  Do we say since you are already in middle of doing a mitzva therefore you are Patur from helping your father, since "HaOseik BaMitzva Patur Min HaMitzva"?

Rav Shternbuch answers that even in this case your obligation to help your father takes precedence over helping your mother.  The reason is that the preference of your father is not simply a halacha of doing a bigger mitzva.  If it were then you would be exempt if you are already in middle of helping your mother.  However Kibud Eim does not exist at all in the face of Kibud Av because of the mother's similar obligation towards her husband.  Therefore helping your father takes precedence even after your previous commitment to helping your mother.

Important Nore: We try to convey the Tshuva to the best of our ability. We admit that our understanding may not be accurate. Please also understand that this Tshuva may not be the final word on this topic. One should consult a Rav before drawing any conclusions.