Major Tire Damage Wear

We are relocating about an hour away and have spent about 6 hours on the highway over the last week. Last night I noticed a slight wobble that seems to increase the faster we travel. The steering also feels a little loose. When switched cars so I could follow her and observe and immediately noticed sparks coming from the rear tires. As you can see in the attached photos, the inner third of the tires has worn down to the cord and apparently in the space of a week/360 miles of use.

I'm planning to take it into the local dealer shop for inspection and repair, but I am fairly ignorant about cars and don't want to go in without at least some clue about what could be causing this and whether it should be covered by warranty or not. The car only has 37k miles on it and we've never had any mechanical problems or noticed anything unusual until this. The tires were brand new about a year ago and the front ones don't show any uneven wear at all.