There's a rather popular Roman Catholic argument that goes something like this: "Mary is Jesus' mother. Jesus never sinned. The Fifth (fourth for RCs) Commandment is 'Honor thy father and thy mother.' Therefore, if Mary asks Jesus to do something for her, He'll do it out of obedience to his mother."
But consider this: the Church is the bride of Christ. Those of us who are believers, we're part of that church. Now, if we're going to apply metaphorical language, who is in a better position to get a "yes" from a man: his mother or his wife? Maybe I'm overly romantic, but I think that generally the flesh of one's flesh gets top priority.
But let's not rely on that metaphor. Jesus so loved us that he laid down his life for us. Is he really going to deny us any good thing?
And God as for God the Father:
Romans 8:32 He that spared not his own Son, but delivered him up for us all, how shall he not with him also freely give us all things?
So, no one should think that it is either good or necessary to appeal to someone other than God in prayer. Pray to God, not to Mary, saints, or angels. If you are His child, he'll hear you.
If a son shall ask bread of any of you that is a father, will he give him a stone? or if he ask a fish, will he for a fish give him a serpent? Or if he shall ask an egg, will he offer him a scorpion? If ye then, being evil, know how to give good gifts unto your children: how much more shall your heavenly Father give the Holy Spirit to them that ask him?