To clarify some more, I'm wondering if the Reset Bag you obtain through Super Training resets the effects of the Soothing Bag.
No, the Reset Bag has nothing to do with Friendship so that factor does not get affected after use. The Reset Bag only erases the EVs gained on a Pokemon completely to 0 on all stats, nothing more, nothing less.
Source: Experience.
No, it just resets the EVs of the Pokemon you use the bag on. Source
