If the mother sticks with the capitalized NO, then it would require both the lawyers and the fighting, especially the fighting. Even then, based on what you have said so far, your odds are not good.
The fact that your daughter has learning disabilities would not be held against the mother, as long as she is doing what she can. With the fact that she has been getting her daughter tutoring and summer school, that shows she is taking reasonable steps to help her daughter. Unless you can show a particularly needed LD program that is in your school, but not hers, you may have a tough time making that case.
If you fight there will be fighting. And it is usually best to keep the kids out of the fighting and yet your understanding that there is a preference is the only real basis for custody reversal that you are clinging to. Nothing puts kids in the middle of the fighting like making them choose between two parents as the decider, thereby turning against one parent.
Contested custody reversal is extremely uncommon, and usually only happens when there are extraordinary circumstances, such as domestic violence or gross neglect.
Sorry to give you words you do not want to hear. I know you and your husband love your stepdaughter. I'm sure the mom does too. It is a shame that it has to be like this. Divorce stinks.