The International Council of Community Churches and all other Christian denominations will recognize the baptism and First Holy Communion as valid and licit (i.e., legal). Since CITI priests are no longer ministering as clerics within the institutional and juridical Church of Rome, they lack jurisdiction from the Vatican to celebrate sacraments on its behalf.
Your baptism or First Holy Communion will be celebrated in a ceremony in the Catholic tradition, according the rites of the Catholic Faith, officiated by a Catholic Priest. It may be recognized by the Roman Catholic Church as a valid reception of these sacraments, although they will consider such celebrations as illicit.
If being able to receive all of your sacraments within the Roman Catholic Church–that is the institutional “Church of Rome”–is important to you, then it will be easier on you and your child to pursue reception of all of your sacraments within your local parish.
If you receive these sacraments from CITI priests, even though they will be valid and efficacious, the local parish may challenge them on the grounds of being illicit (irregularly celebrated). You will receive a certificate of reception of these sacraments from the priest, and the record of your baptism or First Communion will be recorded at CITI Ministries.