I'm not sure if either of these create the small poos - if either did, it would be more likely that Instinct would bc it's grain free.
 
I don't think the bad breath is related the food at all though, in this case. Has the vet given a thorough look at her teeth? Anything funky there?  
Are the conjuctiva of her eyes red (the lining if you pull the lid out)? Is the discharge greenish/smelly? 
Sometimes things going on in the mouth can irritate eyes too - as in, sometimes when puppies are teething, there eyes drain more; so it just makes me wonder. Another thing I'd suggest is trying PetzLife Gel - I think it's pretty good stuff. 
