Is this about formulas or faith in God that he sees the intentions of the heart?
God sees intentions, yes, which is why there can be “baptism of desire” in situations where a person cannot be physically baptized.
However, the Church can only go by the sacraments as God has laid them down. A sacrament requires valid matter, form,
and intention. In this case the matter and intention were correct, but the form was not.
Your daughter may very well be baptized in God’s eyes. God is not bound by His sacraments and can do anything He wants. However, the Church is not omniscient, and thus requires a record that a valid baptism was performed.
Of course, your daughter is not at fault, and neither are you. The blame lies squarely with the priests who chose to muck about with the sacrament. However, since the Church’s highest authority on such matters has ruled that their mucking about renders their baptisms not only illicit but invalid, your daughter will have to have a valid baptism performed and recorded in order to continue in the life of the Church.
Remember, God also treasures obedience to those whom He has placed in authority, in all matters that are not sinful. Even if you are morally certain that He has already granted your daughter the graces of Baptism, He will not be offended and indeed will be further pleased if your family goes along with the Church’s judgment.
As another poster suggested, it’s possible a conditional baptism would suffice, thus leaving up in the air the question of whether your daughter was originally baptized “in God’s eyes” but still satisfying the Church’s requirements. That might soothe your husband’s concerns.
I’m not entirely sure what “
in forma absoluta” in the Vatican’s response means, though. It’s possible that it would close off the avenue of conditional baptism. Still, you should inquire.
Usagi