rabbiofberlin, Regarding your car trip example: if instead of sweatpants, she used a miniskirt, would that change the metzius of its permissibility? If you claim that tznius is unnecessary when only surrounded by immediate family, then you seem to say that a miniskirt too would be acceptable in that environment.
But even more importantly: is she able to get from her home into and out of the car unseen? When driving, is she invisible to others on the road or street?