Complex sentence: Jack was happy to father the child, however Phyllis was on edge; but she decided to help Jack with the child and at the same time get Diane (who was now aiming to have Jack for herself) out of their lives.
Split into simpler sentences: Jack was happy to father the child, but Phyllis was on edge. She decided to help Jack with the child and at the same time get Diane (who was now aiming to have Jack for herself) out of their lives.