So some thoughts on which paths could be taken with this.
as HJ tulp already wrote a lot of the trouble came from willem I and most of all that moron willem II.
instead of W II keeling over, maybe his liason with princess royal Charlotte results in him becoming prince-consort of the UK crown-princess/Queen.
He wouldn't be able to become king in the netherlands in this situation., so that would mean his brother Willem-Frederik would become king, WF was a very amiable person and very good with people.
so this could have 2 effects at the start britain does return south-africa & ceylon under these conditions, and maybe WF gets Cleves-Mark-Julich-Berg-Cologne as a wedding gift (WF married Wilhelmine von Preußen)
with Charlotte being married to willem the butterflies start flying already, her not marrying leopold of saxe-coburg, means he stays out of the picture, so no reason for him even be contemplated anywhere near otl belgium now.
So you would not only have the united netherlands, but also some added colonies.
edit: plus WF was a rather practical person, he likely would have ended the salic laws in luxemburg, so that later on it could continue to be dutch even with a female successor.
Butterflies but if we got Napy III, 1867 might be seen as an insult at best, a a threat at worst
of course a far out route could be Louis-Napoleon switching sides, and later staying as King of NL.
Nap III is the son of Louis-Napoleon, so in this route no probs with that