In the Radal on the above Medrash he explains what is the meaning of the words that he is a baki in the Torah? It is based on the Gemara in Kiddushin 31a where a widow asked Reb Eliezer if a father requests a cup of water, and the mother requests a cup of water which one comes first? Reb Eliezer responded leave the honor of your mother and do the bidding of your father as both you and your mother are required to show respect to your father. This is the reason why Yaakov was scared and worried to listen to his mother against the wishes of his mother. 

The question one can ask is why is there a requirement to listen to the father before the mother? The reason given is that both the son and the mother must respect the father. The problem is that there is a Gemara in Yevamos 62b that says a man must show respect to his wife. The quote is that if one loves his wife like oneself and honors and respects her more than himself, he is blessed that he won’t come to any sins. The Rambam in Hilchos Ishus 15:19 says that the Chachamim commanded a person to be mechabed his wife more than himself. If so the halacha should be the same as if one’s parents are divorced where the wife has no requirement to respect her ex-husband so the child could choose who he or she wants to honor first, as in that case the honor of his mother and father are equal. Now, in the case where one’s parents are happily married, they both need to show respect to one another so why is the halacha in the Gemara that the child must do the bidding of his or her father? 

One answer is that in the case where both the child and the mother need to respect the father is regarding all the mitzvos of kibbud av where both the mother and son have a requirement to feed the father and to give him to drink and help him get dressed etc. But regarding the respect a husband must show his wife is to make sure she gets nice clothing and have her look respectable but that is not connected to the mitzva of kibbud av therefore one must carry out his or her father’s bidding before the mother. 

Another answer is that the halacha is that a woman must be mechabed her husband al pi halacha. We see this in the Mishna in Kesubos 59b that lists of all the melachos a woman is required to do for her husband. We do not find the same halacha for a man that he is required to do for his wife mitzad halacha. It is just a preferred way of life as the Gemara says if one is mechabed his wife more than his own self he will not come to be chotei. It is just a midas Chassidus but not a chiyuv mitzad halacha therefore a child will have to listen to his father before he listens to his mother. 

The Mitzvah of Kibbud Av Ve’Eim is one of the hardest to do. Let us all hope we are mekayem it properly and thereby zocheh to Arichas Yomim!