Latin priest administers and the Latin faithful receive per Latin discipline in any Catholic ritual Church.
Eastern priest administers and the eastern faithful receive per eastern discipline in any Catholic ritual Church.
“It must be remembered that the law indicates that sacred ministers cannot deny the sacraments to those who seek them at appropriate times, are properly disposed, and are not prohibited by law from receiving them (CIC c. 843, s1 cf. CCEO c. 281, s2). A fully initiated infant is not prohibited by law from receiving Holy Communion, is properly disposed, 101 and has a right to receive Holy Communion during Mass (appropriate time). An Eastern Catholic infant would certainly be within his/her rights to receive Holy Communion in a Latin Catholic parish when there is no Eastern Catholic parish in the vicinity. In addition this child could and should receive Holy Communion if he/she attends a Latin Catholic school during the week and there are no Eastern Catholic schools in the vicinity.”
“Naturally, out of respect for the Latin Catholic discipline, the parents should discuss these concerns with the Latin Catholic pastor beforehand.”
“Lastly, it should be noted that never should the parents of a fully initiated Eastern Catholic infant, for the sake of mere convenience, attend Mass solely in Latin Catholic parishes when there exists an Eastern Catholic parish in the vicinity and have their child receive Holy Communion on a weekly basis. While the child would be withing his/her rights to do so, such a practice should be strongly discouraged of the parents as it can lead to the Eastern Catholic family allowing themselves to be Latinized … strong leadership from a pastor comes in to play whereby the pastor should properly teach the parents about their duties they owe to their own church sui iuris and their duty to raise their Eastern Catholic child in accord with his/her rights. 102”
Comparative Sacramental Discipline in the CCEO and CIC, edited by Francis J. Marini, p. 48-49.