Since you ask--one. I was thirty six and in vitro was offered to us also, but we felt that, perhaps, God had another plan for us. Six months later we became very happy parents of our adopted som.
Look, God's plan for you is fine. We went through a variety of steps in terms of fertility assistance that was short of IVF, but nothing worked. Concurrently we started adoption procedures. We then did a ton of research on IVF and selected a successful clinic that was very open to our concerns. They helped us conceive our other children, and we also continued with the process for our adopted daughter. We are now a big, loud crowd when we go out.
Your initial question was why couples felt the need to have "their own children". The need was the same deep, emotional need that you felt to have "your" children. Having both natural (at least in my opinion, although not the Catholic Church's) and adopted children, I really don't understand the distinction you are trying to make.