Lilyka - Thank you for your clarification about baptism. I was raised protestant, but not catholic, so I'm not aware of the subtle differences. As I was taught, baptism meant that you were dedicating your soul to the religion/belief system/god as it applied to the particular religion. In the case of the OP, I wouldn't feel comfortable making such a choice for my own child. I know that no one is going to hunt a person down for walking away from the religion, but to me, the baptism carries such a heavy religious implication that I just wouldn't be comfortable doing that without the child understanding the meaning of the event. JMHO. I realize that catholics are different than protestants, and actually all religions have their subtle nuances such as you have alluded to.
OP - I don't envy your situation. Have you thought of the many long term possibilities of your actions? How do you think your children would feel as adults about this, the truth of the situation? How do you think they might feel about the truth of the situation with the sneakiness and the attempt to fully immerse them into your own religion and you've not mentioned any desires, thoughts or intentions of allowing your children to grow up familiar with and understanding of the other half of their heritage? It is my vague understanding that baptism is a sort of commitment ceremony. Is there a way you can wait for your children to choose to commit themselves to catholicism? It doesn't prevent you from sharing your beliefs and faith with them, and it allows them some control of their own futures. Yes, your DC's father isn't currently reaching out to them, but with the bit of backstory you provided, the situation doesn't seem honest and I would worry about this coming back to bite me later, it may be in months with a custody battle, or it may be in many years when DC are adults and feel resentment because they weren't allowed to honor half of their beings. Do the benefits outweigh the risks, because the future is unpredictable.
Again, with my humble opinion, but I feel that if a person chooses to cross broad cultural/religious boundaries and have a family with someone of a vastly different background, then we need to honor that, especially in the case of single parenting. I worry about my DD rebelling (when she is older) because I chose to take her and I out of an abusive situation, basically isolating her from her father and his heritage. That is the most simply put version of the events. So as a single mother I feel it is my responsibility to include both parts of DD's heritage in her life and to not necessarily attempt to emphasize one more than another due to my own personal choices/beliefs. This is how I am doing things. I want my DD to know as best as I can offer, both sides of herself. I won't make choices for her wrt to things such as religion. If, when she is older, (she's a toddler now) and wishes to follow one way more than another, then I will be flexible to that too. She is her own person and not something to bend to fit my will or desires. I chose to have a child with someone from a very different background than my own. Just because my relationship with this person did not work out as a long term family unit, doesn't make it feel right for me to ignore 50% of my DD's heritage, whether I approve of it or not. I feel I made my compromise long before she was born.