You can catch the right version... but what about the other one? Besides, your mom even gives you the mega stone for the other one. Is there any way to do it(aside from trading)?
If you can get the Eon Ticket via streetpass, you'll be able to sail to the island where you caught the original Latios/Latias. The other one (Latios in OR and Latias in AS) will battle you, and you can find the Soul Dew after the battle/catching them.