Rims keep bending

There's no way you could 'just reseat the caliper' and all be alright again.
Something is still major 'upped for the caliper to work its way outward like that.
Check the bracket it's mounted too. Check for a missing (large) bolt.
The pins just locate the floating caliper and brake-pads. The bracket carries the brake-load to the spindle, when brakes are applied.

OTOH, I don't see yet how a caliper could bend a wheel like you described, and even when you don't or hear anything 'funny' while driving.