I wonder though, whether she would've had such influence
It's at first glance unlikely of course, but not very far-fetched. The wives of Philip V and Charles IV were very influential. Charles III was very much in love with her and refused to marry again despite surviving her for 3 decades. And they were very fertile and had mostly sons. It is also common for queens to want something for their other children, especially when they have a lot (of males). Finally, this would happen when Charles III is old and kings tend to become emotional. Aranda's proposal happened IOTL after all. Having the queen support it would be a pretty big bonus. Later historians in that TL would also point at Charles III reorganizing the South American viceroyalties like IOTL as a preliminary step in this direction, even though we know they are wrong, so it wouldn't feel like a move coming out of nowhere.
If the thing goes smooth this would leave:
Charles - King/Emperor of Spain
Ferdinand - King of Naples (not Spanish vassal)
Gabriel - King of Mexico
Anthony* - King of Peru
(fictional or a surviving infante Francis because of butterflies; OTL died of viruela in 1771, at 14) - King of New Granada
(fictional) - King of La Plata (maybe inc. Lower Peru/our Bolivia)
With each younger infante receiving a perceived less valuable inheritance than the previous one.
With the islands (Aranda mentions Cuba and Puerto Rico, but let's throw in also Santo Domingo, Trinidad, Guinea, Malvinas and Philippines, and of course the Canaries) still part of Spain proper.
*The smartest of the bunch. Could lead to interesting shenanigans coming the Napoleonic Wars.