Previous news accounts have said that UNNAMED DAD also had a history of domestic violence directed at the mother. So no, he shouldn't have been allowed in the hospital around the mother OR the baby.
http://www.abc.net.au/news/2014-04-01/teenage-father-charged-with-murdering-baby-son/5360194
Teenage father charged with murdering baby son in Bunbury Hospital
Updated Tue 1 Apr 2014, 7:19pm AEDT
A 15-year-old boy has been charged with the murder of his month-old baby son at Bunbury Hospital in WA.
Police allege the baby was critically injured by his teenager father in February.
The baby was taken to Princess Margaret Hospital and placed on life support but died a few days later.
Previously the father had been charged with causing aggravated grievous bodily harm to the baby but that was upgraded to murder during a hearing at Perth Children's Court today.
The death prompted debate over whether the teenager, who was a ward of the state himself, should have been given unsupervised access to the baby.
The head of WA's Department for Child Protection later told a parliamentary inquiry all procedures had been followed in the case.