You are saying that it is a surprise tree.
Irene had 4 children, and Irene was one of 5 children, so there are lots of people who do know about the family, and possibly have already done a family tree. Are you in contact with most of these people to find out further information?
If you want a family tree of her parents, you need to know Irene's father's name also.
Do you want to do the tree by a certain date, or can you wait and buy certificates when necessary?