I'll bet this has happened more times than people realize. My oldest (now 21) was having trouble breathing and then stopped breathing as an infant and the ER doc sent us home because I was "overreacting" and there was nothing wrong. The next day I brought her to the clinic and she was admitted for 3 weeks due to pneumonia (clinic dr said me sitting with her in an upright position the rest of that night after the ER visit probably saved her life). What can a person do about it? Well, of course litigation is one possibility, but, in my opinion, if the outcome eventually is treatment, then what are the true damages (to us Mom's, alot, don't get me wrong)? Certainly, if your daughter will suffer long-term and lasting effects from the misdiagnosis, then you should seek legal counsel. I sent a letter to the Dr. who let my daughter go that evening and carbon copied every person I could think of that would matter (hospital board, licensing dept, etc) and left it at that.
I think the most valuable lesson that comes from this kind of experience is "if you think the dr. is wrong, go somewhere else." Don't feel like just because he/she has a medical degree, he is smarter than you or knows better than you regarding what is best for your child.
Good luck :)