My question is what can I expect to remove with this package?
As a general rule of thumb, you can expect-
A "finishing" polish to take the swirl-free finish to the next level, giving the wet glossy look that is so sought after. Also can be used to touch up light marring like from a buddy leaning on your car then saying "oh, sorry" and wiping the area with his shirt.
A "swirl remover" polish to take care of the spider web swirls that are inevitable on a daily driver. A "swirl remover" should finish marring-free to the naked eye, but still can be improved on.
A "compound" to take care of the worst of your
correctable flaws, meaning that there are scratches that a compound will not be able to correct, like if you can feel it with your finger nail don't get your hopes too high. A "compound" will likely leave the finish marred and will need to be followed up with a "swirl remover" (and then a finishing polish if you desire).
I am afraid I didn't get an aggressive enough swirl remover, or I am doing something wrong.
If your in a hurry, grab some Megs 105 or Ultimate Compound locally for those scratches, the swirl remover isn't "cutting it".

Trying to remove a scratch with a gentile swirl remover to tough at best, Pinnacle ASR is a gentile swirl remover.
How long are you working the area? Do you work the polish until it's just about gone, or is there a lot of polish residue on the paint still when you wipe clean to check your results?
I recommend working on an area no larger than the size of 4 of the pads that are on your machine. Apply the polish to the pad and dab it on the area to be polished in a
12
34
pattern (the size of four pads) then spread at low speed. Polish with the machine at high speed but move slow, count to 10 on each pass. 50% overlaps on each pass, side to side then top to bottom until the polish residue left after a pass is minimal. Referred to as "flashing" the polish residue will become almost clear, indicating that the abrasives have been broken down. IME, It's important to sufficiently work a polish that has
diminishing abrasives to get the finish that is intended. Pinnacle Advanced Swirl Remover has Diminishing Abrasives.