Jack isn't the ideal role model. Convictions for ABH and assault, jail time etc.
At the end of the day, if the kids are happy about it and Jeff doesn't mind, then Jack should play a part in their upbringing. How big that part is, is up to Jeff and the kids.
I can't believe the media are still talking about her ten days after her death. It's about time they left the family to grieve in peace. There are far more newsworthy things going on at the moment than a young mother who has died of cancer.