Clarification on Baptism

I would like some clarification regarding who can facilitate Baptism?  I understand both the person being Baptized as well and the person performing the Baptism must be sincere in their desire to receive this wonderful sacrament.  And ideally a priest or deacon should Baptize.  I also understand the Catholic Church accepts Baptisms from other Christian faiths as valid.  To me this means, Baptism is about being a member of the God's family, not so much a specific christian faith.  Here's my dilema.  My daughter, her husband, and my first grandchild are all Baptized Catholic.  When my daughter and my son-in-law tried to schedule the Baptism of my new grandson they were denyed because neither Godparent is a practicing Catholic.  The Godfather to be is my son who while brought up Catholic is a very active Christian in a non-demominational Christian Church.  He is more Christian than most Catholics I know.  He could have very easily registered at a nearby Catholic Parish but that would be a lie, of course he did not.  I tried to explain to my daughter that if her intention is to have her son Baptized in the Catholic Church, then she must abide by the Catholic regulations.  She does not understand this - both she and her husband are very upset with the Catholic Church (not the first issue she's had with Catholic doctrine).  All this leaves my baby grandson in limbo.  Being that both parents do want their child Baptized and the Catholic Church has refused, I believe this might qualify the situation to be urgent.  Under these circumstances, would I be able to Baptize the baby (now 5 months old) if done reverently and with the best intentions for this child?