Then they'll have to make a new ship for traveling to Mars, and it'll have to have stronger shielding from radiation, too. Even from a solar flare.
That's correct. The six-person crew to Mars will probably launch from Earth together in one Orion CEV, but then move into a Transit Habitat vehicle for the 130 to 180 day voyage to Mars on a fast transit trajectory.
NASA has a lengthy and dry, but useful concept document for a manned mission to Mars on their web site prepared in 1998, including a summary graphic for one possible Mars mission sequence.