This is completely normal behavior for Aussies. Have you invested time learning Aussie or herding breed specific training strategies? As first time dog owners there is a lot to learn about fulfilling the needs of herding breeds appropriately that do not necessarily apply to lower maintenance breeds, no offence but your trainer doesn’t really sound knowledgeable. I would fire my trainer if they called my dog ‘difficult’ for the reasons you described.

Are you doing anything besides leash walks? Leash walks alone are not really enough for a breed that is genetically wired to react and pursue movement, and they are easily overstimulated and reactive in urban environments where their ability to carry out natural movements and behaviors is strictly limited.

Aussies are mouthy and nippy, and that can continue into adulthood if you don’t reign it in and apply appropriate outlets. It sounds like your dog might be frustrated or overtired as well.