Well, couldn’t they simply get her baptized in a Protestant church? Many will do it no problem with little or no requirements, and since the Catholic Church accepts Protestant baptism as long as it’s done in the Trinitarian baptismal formula…
The Catechism of the Catholic Church:
The ordinary ministers of baptism are the bishop and priest and, in the Latin Church, also the deacon. In case of necessity, anyone, even a non-baptized person, with the required intention, can baptize by using the Trinitarian baptismal formula. The intention required is to will to do what the Church does when she baptizes. The Church finds the reason for this possibility in the universal saving will of God and the necessity of baptism for salvation. (CCC 1256)
I must say it’s quite unfortunate that the Priest would take that hard a line. The other option is to simply go to a different Parish or contact the Diocese.