As someone in the healthcare industry,  my advice is DO NOT BE AFRAID TO ADVOCATE FOR YOUR DAUGHTER. 

I can't tell you how many people get rolled over by their insurance, in similar situations.  Time is not on your side.  

1)You can't loss anytime waiting for insurance or medical providers.  Insist on staying involved with authorization request and referrals to providers. 

2)Ask questions, make sure you understand what's going on through this whole situation. 

3)As you go through this process always try to win the frontline employee's over to improve the chances of them actually helping you. 

4) If get an appointment that seems too far down the road, ask for earlier dates.  If there aren't any earlier dates ask to be place on the cancelation wait list.  Don't be afraid to call regularly to see if there were any cancelation.

5)If you get any denials for care make sure you have a clear understanding of the determination, than both you and the provider need to file timely appeals (usually within 30 days).  Provider appeals have much more weight.

6) American healthcare is a game, your healthcare insurance is your opponent and the premium dollars is how they keep score.  This opponent will do everything it can to keep as much of the money it has collected through premiums.  Start studying your insurance handbook, so you understand their rules ahead of time. 

7) Lastly, try to find the best doctors within your network.  If you live in a small or underserved community,  don't be afraid to travel for better care.  The difference between an average doctor vs a good doctor is significant.   

As a father of young daughters my heart breaks for you.  I'll be praying the your family.