The boys were aged 4 and 10. The driver of the car, believed to be the boy's mother, and another female passenger, remain in a stable condition in hospital.
The crash occurred on the northbound carriageway near junction 15 at around 11.25am this morning.
The motorway has now reopened.
More top news
Sean Dyche has labelled as "harsh" the 18-month ban handed to Burnley's Joey Barton for a breach of betting regulations.
A rapist who targeted elderly and vulnerable women as they slept in their beds in Lancashire has been jailed for life.
Less demand for donors means that frequent volunteers won't be contacted as often.