Once the kids are age 7 they are considered adults as far as baptism is concerned, so the parent couldn’t baptize them even if they wanted to. The kids would have to choose for themselves and go through RCIA.
Actually, you are slightly off in what you are contending.
RCIA specifically stands for the Rite of Christian Initiation for Adults. A seven year old would not and could not go through the RCIA program; it would present an absurd situation.
The child theoretically could go through the RCIC (the Rite of Christian Initiation for Children) if such has been established in her parish (which is rare as an existing program) or, more likely, a program would be specially devised for her, probably using elements of an existing religious education program. All this has to take into account the age and maturity of the child and also the particular law governing the administration of Confirmation in the jurisdiction where the child resides.
It is true that Canon 852 §1 defines that one who has attained the age of reason is not to be treated as an infant, canonically speaking, and to judiciously apply the norms of the canons for adult baptism.
This means in practice, however, that the priest who has the
cura animarum for this child has to ascertain if the seven year old has attained the age of reason. If the answer is positive, then he would need to ascertain the child’s understanding and her consent regarding the sacrament. That is to say, the child cannot be baptised against her will. She must positively consent and also demonstrate some level of knowledge and understanding…however attenuated…according to the mind of the legislator in Canon 865. This standard is going to be much different than someone older, however, and care would have to be used in the canon’s application from a pastoral perspective. There are also more factors to take into account relative to religious education and its normal progression for someone of that age.
On the other hand from the judicious application of the adult norms for baptism, it is also true that the child has not reached her majority nor is she emancipated. As defined by Canon 97, our theoretical seven year old is a minor. The same canon tells us when she will attain her majority in terms of canon law.
Therefore, our scenario of applying the norms of adult baptism does not work in the other direction. In other words, if the parents bring a child to me to be baptised and I speak with her and she indeed wishes to receive the sacrament…we may proceed. If she is brought to me and she does not want to be baptised after explaining the rite, or attempting to explain, we may not proceed. (This is an application of the adult norms.) If, however, she comes to me wanting baptism but the parents are opposed, we may not proceed…barring danger of imminent death and the situation envisioned in Canon 868 §2. This is because she is a minor from the perspective of both canon law and civil law.