Some of your 'shortcuts' are not good ideas. Definitely start with cold water. Definitely bring up the temp slowly. Definitely do not boil. Do add aromatics upfront to the broth, but remove them as they get mushy so they don't cloud it.
Standard ratio for beef broth would be: 8 pounds of bones to 6 quarts of water to 1 pound of veggies (onion, leek, carrot) to one 'boquet garni', essentially garlic, rosemary, anise flavoring for pho, and bay leaf, plus whatever else I forgot.
If you have 'pond water', which I interpret as thin-tasting, you probably put too much water in the second time -- this is fixable by slowly evaporating out the water until it gets to a good texture. If you skimmed properly, it will be clear as you do this. I will typically strain through a kitchen towel or cheesecloth as the liquid evaporates down.
I'm guessing you put in like a gallon of water, so you had like three or four times too much water.
As a warning which you probably already know, you are not going to be able to duplicate your local pho joint's broth -- the broth recipe is the thing for pho makers, and they probably have a bunch of tricks they use, including using a neverending supply of yesterdays pho, that you won't be able to do at home. That said, you should be able to get a good beef broth if you follow some basic rules for making stock.
After your brisket is cooked, refrigerate it overnight. This will help it stay solid when you slice it, and will also improve the texture and flavor. Reheat it before serving. If you have time, this will improve many slow cooked foods.
Best Answer
Take everything I say with a grain of salt (pun intended) as I am writing from Texas where we do nobler things with brisket. A true corned-beef-expert would be of Irish or Jewish descent, and from New York.
The meat should have relatively tough individual fibers that separate easily because of the long, wet cooking. It is pretty difficult to overcook brisket as it is so tough. Like Chuck Norris but tastier. Three hours would definitely not be enough time.
It can be fatty and that will be pretty much up to how much of the fat was trimmed off when it was butchered. An untrimmed brisket has a solid layer of fat that can be as much as a half inch thick. Obviously trimmed briskets cost more. The fat can be nice for smoking but the corned beef I have seen is not as fatty.
Fatty and mushy are not the same thing, of course. If the meat is actually mushy then I suspect that it was packed with a meat tenderizer as well as the corning salt and seasonings. If this is the case then there isn't much you could have done differently. Just don't buy that brand next time. Better yet, next time, corn it yourself.