Interesting. I think liberal revolutions will still happen in Latin America and Spain, however the Latin American ones will be even more cautious regarding independence.
The other issue are butterflies: is the compromise between the British and the North American enough to butterfly the French Revolution, thus averting Napoleon's rise to power and the Peninsular War?
If the Peninsular War is averted, then the Spanish king can reinforce the royalist garrisons in the Americas. And, furthermore, absent a French invasion, the junta movement won't get traction in Spain. In this case, we'd probably see some sort of word wide civil war affecting Spain and her colonies with liberals and monarchists fighting in Spain, Latin America and maybe the Philippines.
Note that if the Peninsular War (or any other foreign occupation of Spain) isn't butteflied away, the Spanish American Wars of Independence will take a more civil war approach than a secessionist one (as actually happened IOTL) and a negotiated peace might be on the cards if:
-The liberals take control of Spain
-The liberals negotiate the political power, parliament seats, etc., given to the "American Spaniards". This may also be influenced by earlier British sucess in quelling the (North)American rebellion if that's the kind of compromise the UK did.
Even in this case, however, there is still the issue of managing such a huge constitutional monarchy with early 19th century communications and divergent local interests. IOTL all large states in Spanish America disintegrated and were far smaller than a hypothetical "Democracy where the sun never sets"
If war happens anyway and a compromise isn't achieved, I think events will push for independence anyway and the UK will find in her interest to provide modest help to the Spanish colonies.