we face this all the time. people here often want to go back to Mexico for sacraments, their family are not active Catholics so they seek out a local church that looks Catholic and make the arrangments, when I get the baptismal certificate so the child can prepare for first communion, it is Anglican or some other denomination. The parents are clueless. In this case the child goes through RCIA, makes a profession of faith, is confirmed and receives first communion (preceded by first confesson). Practically their faith formation and sacramental preparation parallel their Catholic peers, and they are only separated during immediate preparation for Easter. But it means a steep learning curve for the parents.
The other common scenario is the parents were not married (or married only civilly) or otherwise were advised to defer baptism of their child because they could provide no evidence of any intent to raise the child Catholic, as they themselves were not practicing. they left in a huff and got the child baptized in another denomination. When the child is brought for first communion essentially the same plan is followed.
I emphasize we do what meets the needs of families here and follows our bishop’s guidelines. the procedure in other dioceses may be different.
a third very common scenario here is blended families, where each child has a different last name, parents are of different faiths, or spent time in another denomination, so some children are not baptized, some baptized Catholic with no faith instruction whatever, some baptized in another denomination. Some are school age, some high school age, some even young adults. And the parents desperately need faith instruction, and help completing their own sacraments, or getting marriages convalidated.
Try explaining to the parents why the sacramental preparation and timing for each family member is going to be different. For all intents and purposes older children, middle grades and up, who are not baptized or have not made first communion are usually in the same “catch-up” class and are separated only when it is time for rites specific to the RCIA. The big difference is confirmation, which is always conferred at the same time an adult (over age 7) is baptized, and usually when a non-Catholic is brough into the Church through profession of faith and first communion.
a bigger problem is children brought for first communion by the Catholic parent who is divorced. The non-Catholic parent shares custody and the child was baptized non-Catholic or not baptized at all, but is being taken to that parents church as well, and by middle school is completely confused. Those cases must be judged carefully, pastorally, individually and the child himself must be interviewed by the pastor to ascertain if he is embracing the Catholic faith himself. These are actually the saddest because of the damage done to the faith of the children. By their teen years these are often to ones who reject the Christian faith altogether because of the conflicting message received from their parents.