Here is the start of my time line.
1458- Queen Margaret gives birth to a daughter, named Catherine after her paternal grandmother. One week later, on March 25 King Henry VI holds a lavish baptism in hopes to reconcile the court; the Duke and Duchess of York serve as Godparents. Later at the Grand Council, the Archbishop of Canterbury manages to work out a complex peace accord to settle all grievances. King Henry also makes the newborn princess the Duchess of Lancaster. The peace does not last.
1459-War breaks out once more when on September 23, the Battle of Blore Heath, the Yorkists army under the Earl of Salisbury defeats the larger force under the Barons of Audley and Dudley.
October 12 the Battle Ludford Bridge, the Lancastrian forces win after Sir Andrew Trollope defects to their cause.
With this lost, the Duke of York and his sons flee to France while the Earls of Warwick and Salisbury flee to Ireland and they are declared traitors.
1460-Catherine is sent to France to the Court of Rene I, the Duke of Anjou, her grandfather, to be educated.
By June the Earls of Warwick and Salisbury along with the Duke of York's son Edward return and are successful at raising an army.
July 10 the Battle of Northampton, Yorkists under Warwick defeat the Lancastrians. The King is found alone in a tent much like the First Battle of St Albans; once again he has fallen mentally ill.
The Duke of York goes to London to press his claim to the throne expecting a warm welcome but the other lords are taken aback by his actions. York quickly produces documents validating his claim to the throne. With this new information, the Lords have no problems with passing the Act of Accord in October; Henry will remain king but York will act as Regent from now on. The Act also removes both of Henry's children from the line of succession instead the Duke of York and his children will inherit the throne.
Queen Margaret is furious with decision and she and Prince Edward flee to Scotland. In exchange for help from the Scots Margaret agrees to hand over the contested town of Berwick and to marry Catherine to James III and Edward to Princess Margaret.
December 30 the Battle of Wakefield; The Duke of York boldly rides out to meet the Lancastrian forces instead of waiting for reinforcement to arrive from the Earl of Warwick. The Lancastrians win and York, his son Edmund and Salisbury are killed. Quee Margaret had their heads are displayed on the City of York's walls.