Holy Alliance intervention in the Americas

Are you speaking of the Holy Alliance created by the monarchist great powers of Russia, Austria and Prussia.

You mean France, the country who had removed Napoleon only few years back and a country who fought all three members of the Holy Alliance.

Well that might be better as i do not think they are in the shape to join their former enemies in a alliance.

Its only going to be a successes if the have the ships to transport men to North America, but in time period you describe neither the Russia, Austria and Prussia had a sea going navies to do that if i am right.

So, how does a "successful" intervention by the Holy Alliance in Latin America affect US and British domestic politics? Could we see the process of democrscy there slow down for a while with the Southern planter elite becoming more powerful in the US and electoral reforms taking longer to pass?

No, but I'm sure that quite a few political leaders in both countries panic in the aftermath.

  I think you may be putting the cart before the horse.  It would require some political change in Britain to prevent it, albeit largely diplomatically, blocking any French intervention in support of Spain as OTL.  As the link for Canning's career mentions, apart from any morale choices this had benefits for Britain in opening up markets in the Americas, which would otherwise be restricted/blocked by Spanish trade policies.  Therefore you would have to assume that Britain for whatever reason stands aside, at least at first.

  If so France is likely to intervene as it highly unlikely be deterred by anything the US says.  The latter lacks the military strength to threaten either France or Spain meaningfully at this point and might be more wary of any such intervention after the costs of the 1812 conflict.  If it does try and intervene it can send arms and volunteers to rebels in Mexico and the Caribbean but probably not much further afield.  Possibly even seek to wage a commerce war against trade.  However the latter especially is likely to prompt a powerful French response.  They could end up having a large force raiding the US coastal settlements.  Which are likely to be sufficiently larger and more destructive than the British raids in 1814.  [If Washington gets captured this time it could well get burnt!  While operating under a Bourbon monarchy the troops and many of the commanders are going to be veterans of Napoleon's wars and likely to revert to his methods in 'enemy' territory.]

  If at some point Britain does intervene that would stop things fairly quickly, simply because the RN is so much more powerful at this point.  If it doesn't then, as mentioned in my previous post the Spanish are likely to have some success until some problems or other result in the drastic withdrawal/reduction of French aid.  Then things could fall apart dramatically, although Spain might hold some continental areas longer than OTL.  [Checking up Peru and Bolivia were only really cleared of Spanish/loyalist forces in 1823/24 so if we assume a French intervention in their aid in 1821/22 the rebels could see some serious set-backs.]

  In terms of US policy in the event the French intervene and the US stands by then I'm a bit uncertain.  The southern plantation holders, who wish to expand the areas open to slavery will look towards Spanish territory in what is now Texas and the Carribean so they might support opposing the French.  On the other hand since conflict between the US and the Bourbon powers could reopen the question of the status of Florida and Louisiana they might be more cautious.  For the rest of the population there might be a general desire to support independence movements but whether it would be powerful enough to prompt them to a war with a great European power while the latter is not distracted by another greater war, which would be a bold step.  also there might be some concern in the north that any such independence states will be vulnerable to southern moves to expand slavery.