Part of the answer to your questions concerns British history. In 1714 Queen Anne of England died with no children. George 1st from Hanover became king of England, as he was the only protestant who had a "blood connection" to Anne. Consequently, George had control over both territories. This also established the heavy duty connection between the British royal family and the Germany states which still exists. I do not know the origins of the running horse wappen for Hanoverian regiments. However, the bandeau...Peninsula, Waterloo etc are tied to the Napoleonic wars. The British king called upon his German regiments to fight with the British army against Napoleon, they formed "the kings' German Legion". They fought alongside their British allies at those famous battles against the French. I forget the date, but Kaiser Wilhelm II awarded these bandeau to the German regiments who fought in those battles. So thus, the bandeau on the wappen of Hanoverian regiments and the "Gibraltar" cuff title for JR 73. The Peninsula bandeau denotes that the regiment fought with Wellington on the Spanish peninsula. Any wappen bandeau was awarded to regiments whether cavalry or infantry, that fought with the Brits against Napoleon. "Waterloo" speaks for itself. Consequently, during WW1 we have the Kaiser (Queen Victoria's grandson" fighting his uncle George and Nicholas his Russian cousin...truly a family affair!
Oh, and lastly, the Yankee rebels here in North American, rebelled against their rightful king George 3rd the original George's grandson! :wink: !