It can sometimes feel that way when you have to wait a long time. The longer you wait the more your fears and worries take over. The more you talk to people the more worried you get, because everyone has a horror story or something they have "heard". Get all that stuff out of your head and just stay focused. You have a great shot just because you were granted temporary custody. That is a huge step in your favor!
But try to stay positive and just keep doing what you're doing. It sounds like you have a great case. If your ex is living in a room-mate situation with multiple other families and you have a stable environment, I would absolutely ask for a home study.
As far as her half-brother, I wouldn't worry about that too much. It can sometimes be tacked on as an "additional positive" when all other things are in favor of that side, but it won't be the sole reason above all other "best interest of the child" considerations. Just make sure that everyone involved knows that you will be supportive in your daughters relationship with her siblings.
You could also ask for a psych evaluation and drug tests if you think that these might be an issue. Just be aware that anything you ask for you also have to submit to, and you will probably have to pay for.