Police are appealing for witnesses after a blue Toyota car collided with a tree on the B2188 Lye Green, near Crowborough.
The collision occurred at 10.50am on Saturday morning (25th November).
It is believed there was an earlier dispute between the woman driver and a man known to her who was driving another vehicle.
A 34-year-old woman and a 15-month-old girl were taken to hospital with serious but not life threatening injuries.
Detective Sergeant Tod Stewart said:
We believe an altercation between a man and a woman occurred on the side of the road before both got back into their cars.
Shortly after, one of the cars came off the road and both people in the car had to be taken to hospital with serious injuries.
We are looking for people who witnessed or have dash cam footage of this altercation or what occurred afterwards to come forward.
A 21-year-old man from Battle, has been arrested on suspicion of GBH with intent and causing serious injury by dangerous driving. He has been bailed until 23rd December.
A 17-year-old boy from Edenbridge, has been arrested on suspicion of the same two offences and has been released under investigation.
If you have any information please report online or call 101 quoting Operation Lifford. Alternatively, you can visit the Crimestoppers website or contact the independent charity anonymously on 0800 555 111.