Depends on the circumstances of both the German Confederation as a whole, along with the aims of Prussia itself. If you intend for Prussia to remain the authoritarian state it is, I'd say they'd be ready to unify German around the OTL time period (1860's or 1870's), although the process may be somewhat complicated by a marginally stronger Austria. However, if Prussia embraces a certain liberalism, the potential for German unification could present itself at an earlier time, depending on how fast the tinge of nationalism spreads across the continent (which might be slowed with the Balkanization of France and relatively weak British influence on the continent).
the prussians have more power as well though, expanded rhineland has many more coal mines and the like. The weaker liberal influence on the continent means more reactionary states, which might actually speed up and strengthen liberal thought(if not in countries, in hearts and minds).
Also, I plan for france to be eventually reunified by prussia in the midst of some war(1830s/40s or , but under prussian monarch and as prussian puppet. This might stimulate unionism in germany, and serve as a precedent.
As for a 'Latin Commonwealth,' unless the states of South and Central America are regarded as equal partners to Spain and allowed to maintain the autonomy they had gained during the Peninsular Wars, it's doubtful that they would wish to cooperate with Madrid.
The liberal government in spain(it might take charge of stimulatin liberalism along with britain and Tyrennia(sardinia)who will be allied)would make those concessions sot that it could focus on improving life for its people. It would make them, however, supply some of their own armies, and in general pay for themselves, while still giving an annual percentage of their income to spain and provide an open market for spain in return for that autonomy. Spain would also gradually try to install puppet governments so it could indirectly control them. And not all of them would get autonomy(cuba, puerto rico, texas, yucatan, argentina and chile south of pataganoia, most islands rould remain colonies for spanish settlement). Slavery would gradually be fazed out(under pressure from britain), but replaced by forced labour for (very
) low wages that is effectively slavery(like pacific islanders in australia were forced to)