Does your lawyer have reports from the school on the tardies, the records of the DUI?
I believe you can request a psychological profile of the mother, but then they do one on both parents and it gets expensive.
I know its difficult to hear the mediator say those things to you, but they are probably right:
The issue at this point is that, unless there is clear evidence that there has been harm to the child in the past or present, it is pretty difficult to fight shared custody unless you have quite a bit of $$$.
You may need to wait it out, unfortunately. Best to do whatever you both can to not speak unkindly of BM- and NEVER in the presence of your stepdaughter. This can be difficult, especially if BM is turning her against you, but try to take the high road here (None of this to say that you ever do- just putting it out there).
And try to stay positive. Also, try not to let this battle consume you both.