T.C.
My daughter dances for Mullane Healy O'Brien, so I'm a little bias but, you might want to go and watch a class at each school first. I can tell you that Trinity is HUGE (number of dancers and in class size); at Mullane, the class size is not that big. At Mullane, all of the teachers are certified; I've heard at Trinity that they have some of the older dancers teach the younger ones- also due to the big class size.
But I would call each school and ask to come and watch a class to see what its really like. You might want to ask around at your daughter's school also. If she goes with a friend she might like it even more. Most irish dance schools run their lessons the same as the school year - so classes won't be starting until the end of this month or the beginning of September. My daughter (12) started dancing 4 years ago and is passionate about it! Good luck!