It was never documented that Ismay ordered more speed, although he probably did, and the official verdict was that the ship didn't split. There were witness accounts that it did split, but the officers said it didn't, so the investigators went with their opinion.

Well at least it put out the fire.
Yeah, I've heard the story but there is some contention about the story.
I also happen to make amateur films, please check them out
www.youtube.com/johncswheatley

If they did, they would have to mention the fire in the coal bunker as well. Not even Cameron had the guts to tell us about that. Titanic left Southampton on fire. And she was still on fire when she sank; one of the firemen declared later on that the fire probably helped the ship go down as quickly as she did, as the iceberg hit her right where the burning bunker was.

The movie was made in 1958, and the prevailing view was that the Titanic did not split until the finding of the wreck in 1985.

Frankly i think this is as good as it going to get. But a movie that includes the investigation would be nice.

Nothing can have the authenticity of A Night to Remember because it benefited from the involvement of survivors.
As far as accuracy, I don't think so. New theories and evidence comes forward all the time. Cameron's film was mostly accurate at the time (for telling a true story) but since that time, we've learned otherwise.
Aside from theories and evidence, we also have to look at it from the POV that a depiction of an historical event will need to be changed in order for it to be a good story. There's never been a 100% accurate dramatization of a real-life event on film. It's just not possible to tell a story like this without there being changes made.
So, no.

It was overall a very accurate depiction, but not a documentary. Some characters/situations were invented (the steward and the little boy at the end), others altered somewhat (the chief baker never got onto the upturned collapsible), and some main characters were composites.
But, as for this:
it was unfortunately hampered by the legal implications of the inquiry. For example they weren't allowed to show Bruce Ismay as pressuring Captain Smith into going faster and not being allowed to show that Titanic split during the sinking.
That is simply inaccurate. There is no evidence Ismay tried to pressure Capt. Smith into going faster that story comes
only
from the speculation of a single passenger, Mrs. Emily Ryerson, whose testimony at the U.S. inquiry was muddled and contradictory, and she admitted she never heard any such discussion, but she had the "impression" they were trying for a speed record. Others present at the time, such as Mrs. Thayer, did not corroborate her story. It became an early version of an urban legend.
It's not a matter, either, of the filmmakers' "not being allowed" to show the ship breaking in two it was simply that all the "experts" in the 50's insisted that the ship had gone down in one piece. The inquiries had no legal import for filmmakers 45 years later. They did provide a wealth of material to draw from.
You might enjoy a Nat. Geographic documentary, "Titanic: The Final Word" (2012) which convenes a panel of experts and they discuss the mechanism of the sinking and James Cameron develops a new animated sequence to show how it broke apart and sank, based on the latest scientific data. They also bring up the question of why the witnesses to the breakup were not believed, despite evidence such as wooden panels and furniture from the interior of the ship floating in the wreckage, indicating a split in the middle.
The sinking of the
Titanic
was an event that has many parallels to a Greek tragedy, and could be the focus of any number of films. I think we won't see any for a while, but so many untold stories accompany the
Titanic
saga, that future films are bound to be made.