What if James II of England had won the Battle of the Boyne(1690)

  Could go either way.  Since he seems to have lead his troops in person there's the danger of something going pear-shaped.  Although a larger war might mean other generals come to the fore a bit earlier, most noticeably possibly John Churchill.

  I presume you got Doug's reference?

  Steve

  Well if they did produce an heir who survived and succeeded them then apart from anything else this likely means no Hanoverian dynasty in Britain.  Which will have a massive impact on both nations and the interaction of Britain with Europe.  Britain will still seek to prevent France or any other power getting too powerful but without a direct link with Hanover it will be markedly less important to the British monarchy.  Also without especially the 1st two Hanoverian monarchs, who still looked heavily towards Hanover there is probably going to be less influence gained by Parliament in that period.  Its still likely to be dominant and unlikely you will see the re-emergence of an autocratic monarchy in Britain but it could maintain some more power and influence longer.

  Duh!  True I forgot about that.  Not sure how stable that union would be as the Netherlands is a lot larger and richer than Hanover, especially at this stage and has long had an active parliament and limitations on royal power.  Could see a lot of tension on trading issues and also where the capital is.  Neither London nor Amsterdam would be happy to play 2nd fiddle to the other I suspect, nor would the respective Parliaments.  However if it worked then you could have a hell of a naval/colonial power.  I suspect the union wouldn't last that long however as neither party would be that willing to concede primacy to the other.  Not to mention questions on language, religion, etc.  It was tough enough at times holding England and Scotland together but the Netherlands as well.

So Britain ends up with a Dutch instead of a German royal family

  If you mean in distance, not by much.  In culture, possibly but because both nations are long established and have clear national identities and interests its probably going to be more more difficult to prevent tension and disagreements.

  The Netherlands is exposed to French threat but so is Hanover.  Its outside the HRE since 1648 but then the Austrians and other German states would be worried by any attempt by the French to control it.  Also its larger and a lot richer even without its sizeable colonial empire.  This both gives greater resources to defend it and makes it even more important for everybody else to keep it out of French hands.  Basically the same reasons why an Anglo-Dutch union [probably only of crowns] would be difficult to hold together are reasons why it would be markedly stronger against a common threat.  Also if Britain and the Netherlands settled their trading and colonial disputes that could save a lot of waste and hassle. 

So what does the current one fall under, true English.