Just FYI, it's
the House
of Mortimer outside of Westeros. Just one of my pet hates.
The thing is, the Mortimer claim was only really paid attention to by the contemporary equivalent of AH.commers. I mean, after the Northumberlands (descended from Lionel of Antwerp) and Edmund Mortimer had embarrassed themselves by committing lukewarm treason, followed by the Southampton Plot in 1415, it looked pretty unlikely that God, luck, wealth or politics favoured these people nd their questionable claim to the throne, particularly as most of the potential claimants were children or women. Remember: the principle of male-line succession trumping all others hadn't been explicitly 'disproven' at this point. It had never come up. In fact, Edward III's entail of (I think) 1376 explicitly enshrined this in... not law, exactly, but close enough. A subsequent entail of Richard II naming the Mortimers as his heirs is only hypothesised, IIRC. So basically, Richard of York's claim was really just situational - a last-ditch attempt to sort out a country that was being, as he saw it, wilfully mismanaged by the people in charge. He had a claim, and he was competent, so he was best placed to take over in the late 1450s/60s. Before this, there would be no reason to marry into a relatively impoverished subject family with a history of treason.
If Henry's brothers are going to have children, they're going to be born in the 1420s-40s. So the older ones are going to be around to take over from the older generation, and the law of averages dictates that some of them aren't going to be complete wastes of space. In this context, Richard of York is a major landowner with some, potentially considerable, political importance, but only something like 10th in line to the throne. Even if the situation becomes dire enough for him to wage war on 'evil advisers' he isn't going to be able to make himself Lord Protector (since the 2nd Duke of Bedford, or whoever, is just as good as him and much more closely related to the King) so he either chooses a few noble enemies (like the Duke of Somerset) or goes the whole hog in 1452 and tries to make himself king. The latter would be stupid, and probably end up in failure, while the former isn't so different to what happened with the Nevilles and the Percies. Depending on how well Henry VI's cousins are at keeping order, he might get away with this, he might get arrested by Ye Olde Feds, or he might just not bother. Same goes for the Percy-Neville feud.
So basically, Wars of the Roses are butterflied. The Dukes of York matter only slightly more than the Dukes of Buckingham.
As to marriages: Henry VI might not be pressured into getting married and having kids, but he probably does these things anyway. The senior cousins marry a selection of Continental women (probably with some connection to Burgundy) and the Gloucesters and the ugly ones marry into the English aristocracy. A couple of spares go into the Church. Since the big internecine conflict is butterflied, the identities of their actual wives don't really matter in a grand historical context. Maybe a half-hearted war with France continues for a couple more decades, but they were running out of money in a big way IOTL.
In the next generation, Henry VI's line might die out and cause a succession crisis, or some cousin might rebel over something, or start a war with Cleves, or become Pope, or invent the flush toilet. The world is your oyster.