If you're after them, you don't need both ho-oh and lugia in your game. I managed to obtain all 3 with only having Ho-Oh and another legendary in my team -- In my case, I used Latios. The mirage spot appeared near Rustboro City.
To spawn the other 2 legendary dogs, I did the following steps:
I went back to a Pokemon Center.
Deposited both Ho-Oh and the 1st dog.
Closed the PC.
Replaced latios with 1st dog. (on succeeding dogs, replace current dog in lineup with last caught dog)
Closed PC.
Withdrew Ho-Oh.
Went back to the mirage.
PS: I'm not sure if it's random but the legendary dog only spawned whenever I add Ho-Oh last in my party.