If we read The Wisdom of Solomon carefully, we can conclude that Solomon never truly intended to cut the child in two. There were two woman who each claimed that the baby was hers. King Solomon said that child should be cut in two by the sword, and that one part of dead child should be given to one women and the other to the second. One woman said that the child should't be killed, and that the other woman should get it. The second woman said: "He shall be neither mine nor yours; divide him!" Than Solomon realized that the first woman was true mother, which was his intention from the start, and ordered that she should take the child.
