The most rational, thinking, mature decision for HK$ would be to take the baby to a Childrens' Hospital Facility for a thorough medical examination/check-up and a few days in a "nursery" environment, surrounded by pediatric nurses, 'real' physicians and dietary specialists.
He is such a paranoid sociopath. What does he have to lose? The baby is eventually going to be given to LB or Virgie. He is making the case for his strange and stranger abduction/kidnapping more severe.
Hopefully there is nothing seriously wrong with Dannielynn and maybe the evil Stern just rushed her to the hospital for something minor to say "see, when people are sick i immediately rush them to the hospital".
During the DNA coverage, it was also reported by one of the staked-out media people that HKS had taken Dannielynn for a doctor's appointment at the same place a week before.