I was playing some Napoleon: Total War and a great feature for the interested history nerd such as myself is the option to right-click on a unit to receive and read not only their specs and stats, but also their historical background and context.
For the Life Guards cavalry, their description immediately mentioned that these men were all of the gentleman class (http://wiki.totalwar.com/w/Life_Guards_(NTW_unit)). My curiosity then branched from this, wondering why gentlemen would want to risk their lives in battle, with glory and honour aside. Gentlemen in the period by definition would be the modern millionaires or billionaires, who could live off of their families fortunes without need to work (usually). Furthermore, why wouldn't these gentlemen on horseback rather be officers of infantry themselves? To my knowledge, the vast majority of infantry officers were of the gentleman class, so I'm curious why the cavalrymen of higher class would rather themselves be privates of horse rather than lieutenants of line.
I'm also wondering what their duties would be from day to day. In Ridley Scott's The Duellists (1977), our introduction to D'Hubert shows him and the other cavalrymen lounging around in a rather ornate room enjoying their pastries and hot beverages, smoking from pipes and reading the times. D'Hubert is then tasked with going to arrest Gabriel Feraud, another officer but of a different regiment, and the story then ensues. Naturally, Feraud was sent to make the arrest because the military of the day was also the policing force which would instil and uphold the laws. So here, we can see some of the duties, but I'm still curious what more there would be for the gentlemen cavaliers of the Napoleonic Era.
Unsurprisingly the Total War Wikipedia page is actually wrong. However the reason for that is that it appears to be copied almost word for word from the Empire Total War entry for Life Guards where it would in fact be accurate.
Before 1788 the Life Guards (or Horse Guards, as they were known) were all styled as gentlemen, this is true. However the first and second troops of the Horse Guards were disbanded in 1788, along with the Horse Grenadier Guards. Most of the gentlemen were discharged during this with the remaining becoming officers of the new regiments that were formed. These were the 1st and 2nd Life Guards that we see in the Napoleonic Wars. They were not all gentlemen and the rank and file were made up of members of the Horse Grenadier Guards and were henceforth recruited via the normal process of the British Army. I.E Voluntary enlistment. We still see the leftovers of this even today with there being no rank of Sergeant in the Life Guards and instead there being the 'Corporal of Horse' rank. However the Corporals were no longer commissioned officers as they had been previously.
Why were they disbanded? Well because having a regiment composed entirely of "gentlemen" does not have a fantastic impact on its fighting ability. The Horse Guard regiments were seen as a big step on the social ladder for the sons of merchants and the like. To such an extent that the regimental nickname was 'The Cheesemongers' and the Duke of York described them as
'the most useless and unmilitary Troops that ever were seen ... nothing but a collection of London Tradespeople'
This reputation lingered for at least another 20 years after their disbandment when in 1808 the Morning Chronicle recalled Lord North's witticism regarding the old Horse Guards
'the only service he knew them to perform, was kissing the Nursery maids and drinking the children's milk in the Park!'
This also brings other points to light. The reason for enlisting and the actual men who enlisted.
Advancement of status. This was a massive part of the society of the era. Advancement and progression through society through appointment or military service was one of the reasons so many men of the upper classes enlisted as officers. To such an extent that when one officer was not selected to command a forlorn hope at the siege of Badajoz he resigned and went home. (Command of a forlorn hope was a sure fire way of getting promoted, the reason for this being that it was so incredibly dangerous that only a handful of men ever survived it and even fewer with enough limbs to make good of it. I simply cannot stress how dangerous it was.)
Secondly we have the men. As you may have guessed the term 'gentlemen' is being used somewhat disingenuously. The Horse Guards were "styled" as gentlemen but the majority of the rank and file were made up of the sons of Merchants. This is basically a potential route of increasing social standing for an emerging middle class. (Other possibilities could be the sons of clergymen or the like.) Not the aristocracy. So these men were not extremely wealthy and whilst richer than most, enough to afford the extra costs, they could not simply retire on a vast fortune.
Day to day duties would be campaign on some other military deployment. I'm not familiar with The Duellists so you will have to elaborate for me but are you sure that they are Household Cavalry? There was a large number of militia cavalry regiments in service during the Napoleonic Wars (men enlisted under the condition that they were not to be deployed abroad) that would have been, as you say, used largely as an enforcement service at home. Some were deployed against a rebellion in Ireland for example.
The Yeomanry is another example of this. However they were specifically gentry and their immediate servants. They were significantly wealthy enough to provide their own horses however their military worth was negligible and this was just another method of advancing ones standing.
Whilst the Life Guards would have 2 troops back at depot in Britain whilst deployed abroad this does not really resemble what you have described so a little more description would be needed for me to identify whether this is just artistic license on the part of the Author. It sounds a lot like Yeomanry to me.
Sources
The British Cavalryman 1792-1815 - Philip J Haythornthwaite
Wellington's Heavy Cavalry - Bryan Fosten