If she has no intention of actually raising the child as a Catholic, and no intention of herself attending a Catholic church, yes I think that almost every priest would decline to baptize the child. Baptism is baptism into Christ and into a Christian community. If they are not going to actually BE part of the community, they should be baptized elsewhere.
I was told that Catholics teach that baptism saves because it conveys baptismal grace so why would a priest deny baptism to anybody who asks?
An Orthodox priest would almost certainly do the same, btw. If there is no intention whatsoever to be part of the community or raised with its teachings, it could actually do a disservice to the infant.
I think the "disservice" part is even more pronounced with Catholics. As I understand it, Catholics have certain obligations to attend mass, etc. and it is serious (mortal) sin for them to not? So while we Orthodox do not have such "obligation" in the sense that Catholics do, basically you are setting the child up in an impossible situation where they cannot maintain what they are baptized into, and as there is "one baptism for the remission of sins" you also prevent the child from deciding later on his own to take this step, since it would already have been done.
Now, speaking from an Orthodox perspective (because I'm not sure what Catholics teach), baptism gives the grace of the Holy Spirit. It is the entry into the household of faith, the beginning of a life of faith, toward salvation. But it is NOT a magical switch at that moment in time that guarantees salvation, without which God cannot and will not save. We don't presume to know anyone's salvation - only God sees the heart. And God is not limited in how He can bestow His grace. And a person who is baptized as an infant must still turn toward Christ himself and live a life of faith - if he hates God the rest of his life, baptism alone cannot be his defense.
Also, while we certainly baptize infants, welcome them as full members of the community who can receive the Eucharist, and have free access to all of the Sacraments, we don't presume God's condemnation of an unbaptized infant who dies. Instead, we trust in His mercy. Otherwise, what of the souls of little ones who die through miscarriage, or accidents during childbirth? We don't consider God to be a callous legalistic toward them, nor that His hands are somehow tied making Him unable to receive them.
The couple (sounds like the mother) is in a very difficult position though. May the Lord have mercy on the family, and restore harmony and unity.