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***”So are you saying that Mary will listen but God is cold and unapproachable?......That Mary will grant your wishes when God might otherwise reject them?......Are you saying that God is bound by the will of Mary?”***

That’s exactly what Catholics say. And lest you doubt, here are some links and examples:

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Now as to the Roman Catholic teaching on the matter:
From the Secret of the Rosary, endorsed by your Popes:
“One day the King fell seriously ill and when he was given up for dead he found himself, in a vision, before the judgement seat of Our Lord. Many devils were there accusing him of all the sins he had committed and Our Lord as Sovereign Judge was just about to condemn him to hell when Our Lady appeared to intercede for him. She called for a pair of scales and had his sins placed in one of the balances whereas she put the rosary that he had always worn on the other scale, together with all the Rosaries that had been said because of his example. It was found that the Rosaries weighed more than his sins.
Looking at him with great kindness Our Lady said: “As a reward for this little honor that you paid me in wearing my Rosary, I have obtained a great grace for you from my Son. Your life will be spared for a few more years. See that you spend these years wisely, and do penance.”
When the King regained consciousness he cried out: “Blessed be the Rosary of the Most Holy Virgin Mary, by which I have been delivered from eternal damnation!”
After he had recovered his health he spent the rest of his life in spreading devotion to the Holy Rosary and said it faithfully every day.
People who love the Blessed Virgin out to follow the example of King Alphonsus and that of the saints whom I have mentioned so that they too may win other souls for the Confraternity of the Holy Rosary. They will then receive great graces on earth and eternal life later on. “They that explain me shall have life everlasting life.” [1] Ecclus. 24:31”

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And get this one. That Her Divine Son might be appeased and softened???????

Popes on the “sure and most efficacious means” for help from heaven:
“We constantly seek for help from Heaven - the sole means of effecting anything - that our labours and our care may obtain their wished for object. We deem that there could be no surer and more efficacious means to this end than by religion and piety to obtain the favour of the great Virgin Mary, the Mother of God, the guardian of our peace and the minister to us of heavenly grace, who is placed on the highest summit of power and glory in Heaven, in order that she may bestow the help of her patronage on men who through so many labours and dangers are striving to reach that eternal city. Now that the anniversary, therefore, of manifold and exceedingly great favours obtained by a Christian people through the devotion of the Rosary is at hand, We desire that that same devotion should be offered by the whole Catholic world with the greatest earnestness to the Blessed Virgin, that by her intercession her Divine Son may be appeased and softened in the evils which afflict us. And therefore We determined, Venerable Brethren, to despatch to you these letters in order that, informed of Our designs, your authority and zeal might excite the piety of your people to conform themselves to them.” (ENCYCLICAL OF POPE LEO XIII ON DEVOTION OF THE ROSARY)
http://www.vatican.va/holy_father/leo_xiii/encyclicals/documents/hf_l-xiii_enc_01091883_supremi-apostolatus-officio_en.html

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I believe that this quote answers that question.
When therefore we read in the writings of Saint Bernard, Saint Bernardine, Saint Bonaventure, and others that all in heaven and on earth, even God himself, is subject to the Blessed Virgin, they mean that the authority which God was pleased to give her is so great that she seems to have the same power as God. Her prayers and requests are so powerful with him that he accepts them as commands in the sense that he never resists his dear mother’s prayer because it is always humble and conformed to his will.... St. Louis de Montfort, in Treatise on True Devotion to the Blessed Virgin, #27, 246.
http://www.ewtn.com/library/Montfort/TRUEDEVO.HTM