If a baby is baptized by one of his parents, without the knowledge of the other parent, is there any way for the baptism to be nullified? If the parent who took the child for baptism had malicious intent and lied to the priest, would that have any impact on the validity of the baptism? Is there a way to "redo" the baby's baptism the "right" way, with the presence of both parents and mutually selected godparents?
Validity of Baptisms
All that is required for a valid baptism (which cannot, due to its fundamental nature, be undone, or invalidated, by anyone, no matter who they are or whatever their rank in the Church—including a Pope), is for 1) water to be poured on the head of the baptized person three times, or that they are dunked in some water, 2) and that there is pronounced upon them the Trinitarian formula, "I baptize you in the name of the Father, and of the Son, and of the Holy Ghost [or "Spirit"]"—3) intending to do what the Church does by her baptisms (confer the washing of regeneration and renewal of the Holy Ghost to a son or daughter of Adam).
These are almost certainly fulfilled by the priest who performed this baptism.
No consent of anyone is necessary for this, and the withholding of consent does not play into the validity of the sacrament. Whether it is licit (allowed, morally OK) to perform a baptism in this or that circumstance is a separate issue. As such, no recourse will result in a 'nullification' of a baptism, unless it was discovered that a priest (or layperson) performing the baptism had another intention than to baptize with Catholic baptism (see above)—and even then, it would still be only doubtful, not definitely invalid, in which case a conditional baptism might be the most prudent thing to do.
But you really ought to be rejoicing that your son or daughter is now a citizen-of-heaven-to-be, and a son or daughter of God! The sins of the men who performed the sacrament should not affect you, as it does not affect the sacrament.
In cases where one feels the validity of the sacrament is doubtful (your case), you can inquire about a conditional baptism—performed as the above, except a conditional clause is included (to make clear that one can only ever be baptized once, and once baptized, never be baptized again—again, due to its very nature): "If you are not already baptized, I baptize you in the name of the Father, and of the Son, and of the Holy Ghost."
Can a baby's baptism be nullified and/or redone the proper way, according to Catholic Canon Law?
The short answer is no.
For an infant to be baptized licitly in an non-emergency situation, at least one of the parents (or a legal guardian) must give consent (c. 868.1 n. 1). This this means in general, if both parents do not want their child baptized, it is not lawful for, let's say, for a grandmother or babysitter to baptize him. True is a grandmother or babysitter does it anyway, and does it properly, the baptism is valid - but it was done in violation of the law.
This is because the parents of an infant have the right and responsibility to make decisions for the child, who obviously is too young to decide anything for himself (c. 97.2). - Can a Baby be Baptized against the Parents' Wishes