It depends upon your group.
Some groups will gladly let you have a very broad trouble, or even a compound trouble; others will want something clear and unambiguous, but might endorse breaking it into two clear separate aspects.
Others still might want you to only have one clear trouble, so as to not "hog the spotlight" with excess trouble that they wind up having to cope with the side effects of. (This last group is probably having some issues with grasping the way Fate Aspects work.)
The Example Given
Some groups won't be comfortable with that particular trouble, as it's able to be invoked excessively as flashbacks when doing too much. (Even your trouble can be invoked for benefit...). This could easily become the "In my time in the klink, I hung out with x who taught me how to y" mode.
Further, worded as "I can't escape my past" can make, in the hands of a bad GM, for a constant drain on your fate points as you keep getting compelled away from the action. For example, a perfectly reasonable compel might be, "As these guys are 49th street gangers, and are out to kill you, you're going to fade out of sight before the party engages." Or, "Since you know he's a vampire, and you mother's friend, you're going to avoid him". Or even, "Oh, look, it's Officer O'grady, who swore he'd plant a gun on your dead body next time he found you in his beat... time to hide!" And that's just the "Take you out of the scene" ones... there are also the "get them first or you'll never win" versions, and the "You owe me" versions.
I'd reject it as a GM for being overly broad, not because the problems are too many, but the benefits too many, and it's too easy for me to abuse it, too. It can make you dance like a puppet on a string.
The problem isn't that it's multiples in one, tho' some groups won't like that.
The problem is that the specific example you're asking about is itself too broad.