is a facility in Pokémon Emerald located just north of Mauville City, on Route 111. Much like Trainer Tower in the Sevii Islands on Pokémon FireRed and LeafGreen, Trainer Hill is a tower designed for Trainers to race and battle through quickly. The concept remains mostly unchanged from the Trainer Tower: each battle mode has a default time and if beaten, offers a rare in-game item as prizes.
If you are referring to the building across that family house, it is the trainer hill
The only other building in route 111 is mirag tower but the place isn't in oras so I would guess that the hill is what you are referring to since it also fits the description of not being in oras