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Your WI concealed carry permission slip has no bearing on FOPA. FOPA addresses the transporting of a firearm from one state where it is legal to possess through states where it is illegal to possess to a destination state where it is legal to possess. FOPA can cover multi-day journeys so long as stops along the way are only incidental to completion of the journey from start state to destination state - gas, meals, bathroom breaks, overnight lodging.
You describe your 17-day road trip as being in at least two parts - WI to Mt. Rushmore, and then Mt. Rushmore to Yosemite. If you stop off along the way to do sightseeing or visiting anybody your journey gets cut into even more sections. If that's the case, it must be legal for you to possess a firearm in each state where each journey begins and where each journey ends.
The biggest problem is CA. Is it legal for you to possess your firearm there? If not, then there is no FOPA coverage for any time you are in CA. Also, the NPS policy is that concealed carry firearms are permitted in accordance with the laws of the state where the park is located. From what you have written CA does not recognize your WI permit so it will not be legal for you to carry in CA either inside or outside Yosemite.