Would a surviving Earl Ralf be offered the crown?
As I suggested above, lets use a POD of 24 Oct 1055 and (yes I think there would be butterflies but) assume for simplicity that events after that date (with the exception of Ralf’s death in 1057) play out the same.
Ralf is a female line descendant (strike 1), Edward designating him heir is no guarantee (strike 2) but the Witan breaking with tradition (like offering it to Earl Harold OTL) means he is in. And yes the attitude of Earl Harold would be crucial as to whether Earl Ralf becomes King Ralf. I agree relations between the two appear to have been friendly and Harold’s power and networks of patronage means he will smooth over any dissent arising elsewhere in the kingdom.
There may have been animosity between Ralf and Ælfgār but I don’t know if that would have extended to his sons Edwin and Morcar, especially as it seems Ælfgār was the disagreeable party. Then again maybe the differences of opinion between the two stem from Ralf being a Marcher lord and therefore in conflict with Ælfgār’s Welsh allies. Edwin and Morcar probably would support Edgar but (based on their “support” post-Hastings OTL) it would be lukewarm. As for Edgar himself – I think if handled correctly he would be a loyal supporter of his first cousin once removed. So King Ralf is “secure” from any internal threat.
Externally however, as noted already: King Harald III Sigurdsson (aka Hardrada) of Norway; King Sweyn II Estridsson of Denmark.
And then there is Duke William II of Normandy, first cousin once removed of The Confessor on his mother’s side which actually makes him Ralf’s second cousin. As an aside, Ralf’s brother, Count Walter III of the Vexin and his wife Biota both died in August 1063 while “guests” of William. I’m not saying William poisoned them but their deaths were convenient because they did not figure into the Dukes plans for the counties of the Vexin or Maine, which Walter had a claim to through his wife. (A still living Ralf should have been the next Vexin count – I wonder why his son Harold never pursued it OTL?)
The Confessor allegedly promised the Duke the English throne, some say while Edward was still in exile (yeah right, when William was 13yo and struggling to stay alive in his fight for the dukedom) or later in 1051/52. There was no meeting between the two at this later date (William was still fighting for control and couldn’t pop over the channel) which suggests the “promise” was conveyed by the embittered Robert of Jumièges, the Norman Archbishop of Canterbury when he went into exile. Whatever the validity of Edward’s promise, it does seem highly likely that while Harold was William’s ‘guest’ in 1064/5 an oath was extracted from him to uphold the Duke’s claim. I apologize if I sound like a broken record but William not having the casus belli like he did OTL will not stop him from having a tilt at the crown of England.