Tire cupping - Suspension -- specifically, ball joints. The axles MAY by a culprit; however, if you run through an alignment to they should check for ball joint play on the front. Front cupping can be balance; but more likely ball joint play.

Now, one check for alignment will also determine if you have and axle problem. Mostly, that is performed on the front as tat is where the most likely wear is experienced.

If your cupping is on the rear, there is a potential for the rear axle to be bent. The same gage check used on the front can be used on the rear to determine if the axle is bent.

IMHO, most mechanics will to the minimum of balancing and rotating tires. Few have an alignment rack to check for axle and/or ball joint issues.

On your other issue, if the computerized system is resetting itself, something is wrong. One or more sensors could be questionable.

Doing an emissions check while a check engine light is on is not a good move. It is a sure sign of failure pending....