Like it says up top, what if Edgar the Ætheling became king.
During 1069-1072 there was rebellion in the north against the conqueror. So to have a bit of drama, the war ends in open battle between in which William dies in the process. With William dead, Edgar is taken to Winchester to be crowned.
Edgar and Robert were great friends in otl and so even with these events they remain so. So he can solidify his position, Edgar marries Cecilia, the eldest sister of Robert. While Robert marries Christina, the sister of King Edgar.[1]
Would Normandy remain under the English crown or would it gain sovereignty? (assuming France is out of the equation for the time being)[2]
Would the invasion of Wales continue? [3]
What would be the political situation with Scotland, do they recognise Edgar as Bretwalda? [4]
How is the next century or so effected or likely to be effected?
Will the church in England break from Rome? [5]
Would this split include other regions like Normandy? [6]
1) Both of these women became nuns IOTL, so it all depends on whether they entered their nunneries before or after c.1070. But yeah, Robert Curthose certainly has more than enough sisters for Edgar to marry one.
2) Hell no, Normandy was always a French fief. This isn't CK2 , where you can only serve one suzerain - Normandy was never part of the Kingdom of England in OTL, it was merely owned by the King of England as a simultaneous vassal and equal of the King of France. Obviously this masks a lot of power play but on a legalistic level, Robert Curthose continues as Duke of Normandy under the suzerainty of the King of France. Since the Capetians were almost powerless at this stage outside the Ile de France, the Normans have basically free reign until the long-term process of centralisation brings them to heel.
3) Uncertain: most of the OTL conquest was down to the influx of a new class of feudal warlords into the newly 'lawless' Marcher region (which had been governed by ealdormen previously). With the Normans sent packing, this wouldn't happen, so there is less pressure among knightly society to 'go West, young man'. But on the other hand, there had been a noticeable rise in Anglo-Welsh friction recently, for example Harold Godwinson's campaigns in the 1060s, and there was also French settlement in the West of England before the Norman Conquest (e.g. Ralph the Timid, who came into conflict with the Welsh) so cross-border friction probably continues in a radically different way.
4) Bretwalda is a load of BS. It wasn't a title that people actually bore, only given to exceptional kings after their deaths. Bede may even have made it up whole cloth. However, the Kings of England had received homage from other Kings on these islands since the time of Athelstan, but this is clearly a quid pro quo situation. During the High Middle Ages, the Kings of Scotland often refused to give homage to the English Kings, and when they did, it was almost always in regard to the Honour of Huntingdon, except when they had been utterly defeated in battle or something. Malcolm was Edgar's brother-in-law, so he may humour him with a little ceremony of fealty, but they both know that Edgar can't actually tell Malcolm what to do, and he'd be insane to try.
5) That tended not to happen - even the Schism between the Catholics and the Orthodoxies was only in the very recent past and was treated as a ludicrous possibility right up until it actually happened. And remember, the Great Schism was backed up by several centuries of theological and cultural differences, which simply didn't exist in England, especially not after the Synod of Whitby. Furthermore, people took the Pope and Inderdicts and so forth very seriously in those days, so no King has the temporal power to convince an entire country to follow him out of communion with the rest of Christendom
voluntarily before the Renaissance - and to throw his toys out of the pram just because the Pope bet on (and blessed) the wrong horse, Edgar would have to be bloody stupid indeed.
6) Even if there was a split, why would the Normans follow the guy who just threw them out of England towards the certainty of Hell? Edgar and Robert might be BFFs, but even so, it isn't an Aragorn-Boromir-death-scene relationship.