I'm going to go against the grain here. First of all, I agree with scottishmummy - you seem to be taking a great deal of enjoyment trotting out his past mistakes and stupidities... even though you prattle on about how it's embarrassing and you'd rather not say it... then you do go ahead and mention it.
I cannot believe you feel it is you right not to let your mother know what is going on. If he were my son, regardless of the trauma involved, and you made the decision not to tell me about it, and he actually DID commit suicide... I'm not sure I would ever forgive you. Do you think, if he does it, that she will thank you for that? I doubt it 
... It says a lot about you that you feel it is your right to say "oh he's full of rubbish" and withhold the information from his mother as well as advising the ex-girlfriend to leave him to it basically.
You go on and on about his prior history, but you know what? When someone threatens suicide, do you think emergency services says "oh well they've got a colourful history, they're probably bluffing.." No, they don't. Because you can't tell someone who is going to from someone who isn't ... until it's too late. I worked in emergency services for years in the states, to people who have overdosed and called for help, to people who have literally had a gun at their head, to someone who was sitting in their car with a hose from exhaust to window and just wanted to speak to someone on the phone so that she wasn't really "alone" when she died. The biggest mistake you can make is to assume because they've pulled shit before that they're not serious this time. Because lots of them threaten numerous times before they finally work up the nerve. The threats can be like "testing the waters" to see how it sounds saying it. Because it might be running around in their head, but they're afraid to verbalise it. And if you ignore it at just the wrong time, someone could die. This nonsense about "oh it's the quiet ones that don't threaten, they actually just do it, that you have to worry about..." is just that - complete and utter nonsense. Stupid rubbish that people say that is absolutely not true.
You DO sound far too engrained in his life. It's like you watch him, like a voyeur through fb and such, waiting for him to mess up, so you can gloat about what a numpty he is and make yourself feel smug and better about yourself and your own life. So he's been stupid and isn't perfect. Are you perfect?
So bottom line, yes I think YABU about not telling your mum that your brother is threatening to kill himself. And unbelievably cold and heartless on your mother's behalf. And I hope to God for your mother's sake that nothing happens, because if she finds out you knew and did nothing, it's not going to go over well. And I say this from the viewpoint of having a seriously screwed up problem sibling myself that has gone through many many of the same types of things as your brother, including threatening suicide numerous times, for which I did everything I could each and every time, regardless of whether or not I actually thought they were going to carry it through. THAT is my responsibility as a sibling.
Sitting back now, and not caring if flames fly. 