Children follow the rite of the father. If you are canonically Roman, your children must be baptized in the RC church. I’m sorry if this is not the answer you wanted to hear, but many priests will “look the other way” and bend the rules which is not the right thing to do.
This happened to my husband and didn’t find out the truth until we were engaged and planning our wedding. My FIL was raised RC, but after marrying my MIL, began attending her Byz Cath parish. When DH was born, he was baptized in the BC rite, contrary to canon law. We assumed we had to get married in the BC rite, and went to see the priest to begin adding preparations. He’s the one who questioned DHs rite, by pointing out his very Irish last name and hinting at how rare it would be for a man of Irish descent (FIL) to NOT be RC. Come to find out, FIL never transferred rites, thus DH was not BC.
This was shocking to him, and we were married in the RC church. After our wedding, DH began the process to transferring his rite so that legally speaking, he’d be BC. That was an interesting process, especially as the eparchy first thought he was just some random, attracted to the smells and bells of the east!