There is a thread where in Eleanor of Aquitaine dies earlier, what if Henry II outlives Eleanor of Aquitaine since she dies in captivity in 1189 and survives until 1213, remarries and has further children with Alice of Vexin, assuming that Richard the Lionheart still dies in 1190's , with John in his late 40's and Arthur in his mid 20's at that time of Henry II's death, who will be the King of England instead...
There has been no evidence to an illegitimate child of Henry II and Alice of Vexin, while other illegitimate children; such as Geoffrey (later Archbishop of York) and William (later Earl of Salisbury) were acknowledged.
Henry's family was divided by rivalries and violent hostilities, more so than many other royal families of the day.
The succession highly depends on who the king appoints:
- If he appoints Arthur, duke of Brittany and the son of Geoffrey II, Duke of Brittany, Henry's "oldest" son to have a son, Henry and Richard, died childless. He could up set Prince John and his sons from a second marriage and would not be seen as a punishment especially after his father Geoffrey, had openly rebelled against Henry II in 1173 with his older brother, "Young King Henry".
- If he appoints, Prince John, as his only surviving son, who lives in England and has a son and heir, Prince Henry of Winchester, he will be setting up a bad precedent.
- Appointing a son from the new marriage, Prince Henry of Kent, could see a big divide in the nation similar to the War of the Roses.