I do understand what you say about the choice of having children. I, too, was terrified. They are a BIG emotional responsibility. Yes, there will be times when the worry for them is such a burden, that you feel overwhelmed. It happens, but its worth it though for the good stuff they can bring into your life. My son wasnt planned, but if I had to do it again, I wouldnt change anything.
Things in our life can get rough sometimes, and that can reflect on others in our life, including our pets. But were doing the best we can do. I just try to accept that the best I can do is good enough, even if it doesn't seem that way sometimes.