I find this idea of James, Duke of York, dying in battle intriguing namely because he would be remembered fondly as fighting for his country and in the future better than his brother who didn't produce an heir but a lot of bastards.
However as to whom his daughters would marry several things already have made do some research into the subject.
The OTL marriages of Mary II/William III and Anne/George resulted in 20 pregnancies between them with only one child, William of Glouster, surviving past infancy. So would switching marriage partners to Mary II/George and Anne/William III do anything?
I'm not an expert in genetics, fertility, and etc after thinking about it, I've come up with a few things to consider:
1) Being first cousins and thus genetically close might have resulted in miscarriages for Mary II & William III. I know other first cousin marriages (or other close relationship marriages i.e. the Habsburgs) were 'fruitful' however just because others were doesn't mean that this marriage would be necessarily like those. The Habsburg genes might have been better to result in successful pregnancies between two relatives than those of Stuart descendants.
2) The marriage of Anne and George resulted in 17 pregnancies but in only six live births of which only the aforementioned William lived past infancy. Of the 11 'unsuccessful' pregnancies, 7 resulted in stillbirths. Most of the living children were sickly and William suffered from hydrocephalus (it was a miracle he lived as long as he did). While considering the medical knowledge and other factors of living in the late 17 century, I think Anne and George might have been able conceive and bring to term but maybe surviving might have been a problem. That problem happens today with couples even with our medical knowledge. (I have friends who unfortunately have this problem)
3) One cannot discount that while they were sisters that Mary and Anne could have been exact opposites in some genetic factors when it came to pregnancies. However the fact that Mary did conceive 3 times rules out infertility. Switching partners might have proven to be better genetic matches.
If Mary II and Prince George (Jorgen) of Denmark had been married in a timeline in which the future James II dies in 1665 then while no one can be certain, I think it would have started the House of Oldenburg in British history. While Charles II might have made the match with the insistance of Louis XIV, the fact that George was a strict Protestant (Lutheran) and was adverse to becoming King of Poland when Louis XIV threw his name into the hat because he didn't want to convert would have been satisfying to the Anglicans. Being the third son in the Danish Royal Family would have avoid continential affairs because of the deaths that would have to happen to result in he or his descendants succeeding to the Crown.
Would a match between Anne and William III of Orange resulted in the continuation of the House of Orange? Possibility, they would have been first cousins like Mary & William, but considering how many pregnancies she had with George it might be that Anne & William would have issue.
So how would this all come about? I think in between 1677 (the year she married William in OTL) and 1680 (when she turns 18), Charles II starts looking for a husband for HH The Lady Mary (of York) who would be acceptable to the English and Scots as Prince Consort since she will likely succeed him as Queen. Being friendly with Louis XIV and somewhat under this thumb, Charles II knows that a Catholic as Prince Consort and/or Regent to any underage successor to Mary wouldn't be tolerated but any Protestant his friend Louis XIV wouldn't have a problem might be nice. Louis XIV suggests Prince Jorgen (George) of Denmark who had been his candidate for the Throne of Poland in 1674 BUT had been adverse to the idea of converting to Catholicism (a Kingdom wasn't worth a Mass in his case). While Charles can't stand George after meeting him, the English and Scottish nobility while liking Charles' nephew William III of Orange (who is somewhat campaigning for the throne) have no problem with the strict Lutheran Danish prince even though it is unofficially known that Louis XIV prefers him.
The marriage doesn't happen until after Mary turns 18 (or when her majority is, I've read that for females it was 16 or 18 during this time) in 1680 because of George being 9 years older, Charles II doesn't want her husband to control her during any 'Regency'. However if she had successed while under 18 but so close to her majority she could have proclaimed her majority with no challenge. In any case I'll say the marriage was in the summer of 1680 with the newly minted HRH Duke of Cumberland marrying HH The Lady Mary (of York).
Probably to satisfy his nephew and appease some of the ultra-Protestants in England and Scotland, Charles marries HH The Lady Anne to HRH William III of Orange in 1663. William III from a political standpoint not happy marrying the 2nd-in-line to the throne, is given a concession: If Mary dies without issue or her line fails the line of succession would be 1-William and Anne reigning jointly, 2-William (if Anne has died), 3-Any children of Anne and William, even though via their mother they would technically be ahead of their father (this prevents William from being the political joke of Europe for being just a reigning Prince while his son or daughter is a King or Queen), and 4-Any legitimate children of William if he remarries.
However much William might secretly pray for his sister-in-law/cousin not to conceive (ironically Louis XIV might publicly pray that she does), I think Mary & George have surviving issue thus resulting in England-Scotland/Great Britain being ruled by the House of Oldenburg. What does this do in reality?
1) The German practice of His/Her Royal Highness replaces the English practice of His/Her Highness almost 30 years before George I brings it with him from Hanover IOTL. (While he is not an enviable man, Prince George would want his children to have an equal title to their cousins in Denmark and Holland)
2) The names of James and Charles continue to be acceptable names for English-Scottish princes with the addition of George, Frederick, and Christian to the already established names used for princes.
3) No Glorious Revolution, which bring up the following questions:
1) What of the Declaration of Right and Bill of Rights of 1689, which to name a few things resulted in barring Catholics from the throne and transfering some powers from the Sovereign to Parliament?
2) Will England and Scotland merge sooner, later, or around the same time as OTL without the question of if Scotland would let the exiled Jacobins rule them when Anne dies?
3) What are the effects of not having an English-Scottish/British ruler with territory on the continent from 1689 to the 1830s do for the political and ecomonic fortunes of England-Scotland/Great Britain as well the European geopolitical structure?
While there might be other questions those to me are the most important.
I'm going to continuing working this is interesting. I know there are somethings I didn't touch upon concerning the health of those involved(the theory that Anne passed haemolytic disease to her children resulting in low survival rate, or the theory that the weaken health of his children was the result of Prince George suffering from syphillis, or that after her last miscarriage Mary II was taken ill that apparently made her upable to conceive), but I didn't because there was no really substantial evidence to go on that I've found at this time. Also what of other Protestant princes? (No Swedes, some otherwise eligible German princes had been given duchies by their fathers) OR what if Charles II had looked for an English or Scottish Protestant noble to marry his neices to? (Though probably more of a political hornet's nest than finding a suitable foreign Protestant prince)
Opinions? Criticism?
I'm interested to hear
P.S.- Because I brought up being first cousins might have influenced Mary & William's unability to produce issue IOTL that might relate to any possibility of Anne & William producing any issue ITTL, I forgot to mention that in OTL Anne & George were second cousins once removed and I must acknowledge that even though they were related further apart it might have had an influence on the health of their children considering I have Mary & George marrying ITTL.