احسن الله إليك If I travel for a month and I’ve a house there to reside in so I won’t be considered a traveller once I reach my hometown then am I still supposed to shorten the prayer while staying there for a month? As I intend to come back?

This issue it depends on whether that place is considered for you as a place of permanent residence or not, even if you were living between 2 places, so if it was then you are not excused as a traveller if not then you are. Also, i have seen different views regarding as some considered the house to be residence and the majority didn't do so and made revolve around permanent residence.