Former TV presenter Anna Ryder Richardson and her husband Colin MacDougall will stand trial later this year accused of health and safety breaches.
It follows an incident in which a child was injured during a visit to the Manor House Wildlife Park in West Wales, which the couple own.
The boy spent three days in intensive care after a branch fell on him in strong winds in August 2010. His mother was also injured.
Former Changing Rooms star Ryder Richardson, 48, and restaurateur husband MacDougall, 46, both deny breaches of the Health and Safety at Work Act 1974.
Their jointly-owned company, Manor House Wildlife Park Ltd, also denies two breaches to health and safety legislation.
Defending MacDougall, solicitor Andrew McLoughlin said: "This is an extensive case based on risk. There are a large number of trees to be considered and criticism to be answered."
Representing Ryder Richardson, barrister Ben Compton said: "There is no dispute a tree came down. The question is about why and risk."
A Pembrokeshire County Council spokesperson said: "Proceedings have commenced against Manor House Wild Life Park Limited for alleged breaches of Health and Safety legislation.
"The prosecution brought by the public protection division at Pembrokeshire County Council relate to an incident which occurred on August 24, 2010, when a tree in the wallaby enclosure fell causing serious injury to a mother and young child.
"The company, the company secretary Colin MacDougall and company director Anna Ryder Richardson each face two charges of breaching section two and three of the health and safety act 1974."
Mother-of-two Ryder Richardson and her husband moved into the 52-acre Manor House Wildlife Park in Tenby, Pembrokeshire, four years ago.
The case was adjourned to stand trial in November at Swansea Crown Court.