When you change a kingdom's law, everyone who has counties in the de jure lands of that kingdom gets to vote on it, whether or not they are your vassals.
As for what to do, focus on marrying your heir/children to either create beneficial alliances or bring good-stat characters into your dynasty, or ideally to bring new lands into your control. For example, if you can marry your heir to the heir of a certain nearby duchy, do it. Then you may have to assassinate other potential heirs to make sure the land will pass into your realm. Fabricate claims on neighboring counties to expand your realm. Declare war on parts of de jure Scotland that you don't control using the de jure claim CB. Make sure your vassals like you and give them gifts/educate your children/press their claims/use the intrigue decisions to make them like you more.
It's definitely very enigmatic when you start playing, for me it mostly trial by fire and reading these forums/ Meneth's wikia guide that helped me get a better grasp. Of course, sometimes things still happen that I don't understand but I can usually retrace what went wrong.