Firstly, I would gently ask her to tell you how she fell. If the answer sounds "rehearsed" that is often the clue. If she is hesistant to discuss it at all, that may be due to the fact she is so traumatized by the injury or she is afraid to tell you precisely what has happened. Also, casually ask her who else was at the playground. If you know these people, you may be able to ascertain if anyone actually witnessed her fall.
My first advice is to request the x-ray films from the radiology dept. of the hospital she was initially treated at. Simply call, state you are her Mother and you would like the films to bring to a doctor's appointment.
Did her Dad have most arrangements with the surgeon? If so, you may want to take the films to another orthopedic surgeon as ask him or her, if the type of fracture is consistent with a fall or could it have been a result of child abuse.
Having worked the ER in my career, there is a definite pattern in fractures as a result of arm twisting.
If your husband has been abusive in the past and it has been documented with the police or child protective sevices, you do have the right to notify them of this injury.
Having an independent opiniion from another doctor would be a good start.
Also, if you can find the name of the ER physician who first saw her, you can call the ER and find out when he is next working. Do not discuss the issue over the phone. Also ask to speak to the nurse on duty. By law, if they suspected child abuse as medical personnel they are obligated to contact the authorities.
While any type of fracture can be the result of child abuse, certain fractures are much more specific for nonaccidental trauma. For example, spiral fractures are most common in child abuse cases.
http://www.aafp.org/afp/20000515/3057.html
As her Mohter, you may just want to drop the discussion at this point. Let her get over the initial trauma, but then, I would make an appointment with a child pyschologist. I would express my fears to him or her and ask if it would be possible for your daughter to be evaluated.