Robert’s Rebellion initial purpose was to remove, maybe kill, Aerys II from the throne. What was their plan apart from that? Had Rhaegar apepared and returned Lyanna to Robert, would the Rebellion let him be king? Were they trying to pass over Rhaegar from the very beginning?

Well, it depends on whether you’re talking about Robert’s Rebellion or the Southron Ambitions conspiracy, because the former was a lot more ad hoc: they wanted to overthrow Aerys because:

• he’s ordered the deaths of Robert and Ned, so they are trying to preserve their own life and Jon Arryn is outraged that he’s been commanded to breach guest right and kinslaying taboos.
• he’s killed Rickard and Brandon Stark (which makes it a matter of revenge for Ned), Elbert Arryn (which makes it a matter of revenge for Jon Arryn), Kycle Royce and Jeffory Mallister (which makes it an issue of the feudal social contract), and all of this without trial, which makes it a massive breach in the feudal social contract.

Yes, Lyanna was there as an inciting incident and propaganda issue (and both Robert and Ned wanted to rescue her from her abduction), but if Lyanna had never disappeared and Aerys had just had another paranoid episode, the Rebellion would still have happened.