One thing I don't understand in your post: given how ridiculously far away these black holes are, how could you possibly even dream of triangulating them with two facilities on Earth via parallax...?
The assumption here is that no force has acted on the energy arriving enough to distort two arrays on earth.
No physicists here but you don't seem to be either. Irc from what had been said with the first event gravitational waves pass through matter and aren't disturbed like em waves, that's why they supposedly open new doors. Secondly, just take it at face value, if they say so it is so, it might seem improbable and "horribly prone to manipulation" but they probably thought of that and have machines precise enough to compensate for whatever effects you or me imagined e.g. "LIGO is designed to detect a change in distance between its mirrors 1/10,000th the width of a proton"[1]. It's like your grandma, never having touched computers, expressing opinions on the next release of some developer tool.
Also they travel at the speed of light, the rotation of the earth is pretty much constant (if not negligible).
The Virgo detector, outside of Pisa, is in the final stages of installing its advanced instrumentation. With LIGO+Virgo a source like the first detection, from September (a very loud event), could be localized to a patch of sky about 10 square degrees in area.
Wow, that's much bigger than I expected. So basically we can only determine the general direction?
With current-generation detectors installed at three stations which is all we can hope to achieve at the current level of funding in the very near future.
More money, more detections at lower energies, better idea where they come from. There are plenty of instruments in cosmology, astronomy, and physics that have already been designed and planned out, but which do not have the funding to be built; Wait 20 years and five percent of them might come to fruition. You could pour trillions of dollars on these problems without running out of novel questions that we've already proposed ways of answering, and novel results from exploratory instruments we've already proposed building. We spend about 30 billion a year on basic science research according to the NSF, spread over all fields. For comparison, the military gets upwards of 600 billion.
We have good ideas about how to make gravitational wave detectors much, much better, but not how to make them much, much cheaper.
> So basically we can only determine the general direction?
10 square degrees is about 0.3% of the full spherical sky.
I used the word "parallax" poorly to refer to the offset between the detectors - localization is most definitely not done via parallax. It's arrival time + some signal processing, so with two detectors, resolution is limited.
Additional details and an image depicting the improvements made by adding a third, properly positioned detector are available at: https://www.ligo.caltech.edu/news/ligo20160404