As for if they will take her or not, talk to the hospital and ask.
A PR mother with a valid OHIP card should be covered but there is also a possibility to lose OHIP coverage through not staying in Ontario even though the OHIP card is still valid. If that is the case here and she uses the still valid OHIP card to get health care covered and if OHIP later finds out that she should not have been covered because she had not been living in ON, they could back charge her for the costs they covered.
As for private insurance, if she is covered by OHIP, she would not need it as OHIP would cover all costs. If that is not the case, you would have a hard time to find private insurance that will cover pregnancy and child birth for a woman who is already pregnant because it is a pre-existing condition. The newborn will be a Canadian citizen and will have OHIP coverage from birth.