Explain your theories of liability

A family’s father murdered a CEO and died, his chilren surffered in this. This as a case between family A and the film company. The film copany want to produce a movie about this murder. Once the contract was signed between the family and True Films, the movie company asked whether the family had any of family pictures with their father and news accounts of the events involving the attempted murder. The family found a suitcase in the garage filled with clothes, and newspaper accounts about the event. The family had mixed feelings about releasing the materials, but they were willing to consider the request by the film company in the spirit of cooperation. Because the filming was about to start, the film’s Director asked if he could at least review the materials while the family decided what they wanted to do about the items. The family honored this request since the Director was only going to look at the materials.
Over the next few days, a number of letters were exchanged between the Film Company and family about use of the documents. Because of time deadlines imposed by the production schedule, the Director went ahead and unilaterally used the materials in the film assuming that everything had been worked out between the parties. The family had initially submitted an offer to the Film Company to use the materials, but then they changed their minds. However, the master copy of the film has already been sent to the film’s distributor for copying and international distribution. 
The family wants to prevent the showing of the Film and hold True Films liable for the actions of the Director. After all, they never gave permission to use the materials in the film and now the film is filled with their memorabilia. I have pieced together the following sequence of events for your review.
On September 5, Dr. Smart, on behalf of the children of the decedent, mailed a written offer to True Films allowing for the use of the materials in the film in exchange for $10,000. The letter gave the film company five (5) days to accept the offer or else the offer was revoked.
On September 6, True Films received the letter from Dr. Smart with the offer.
On September 7, the family changed its mind about granting permission to use the materials in the movie. Accordingly, Dr. Smart mailed a second letter to the film company retracting the original offer.
On September 8 at 10 a.m., True Films received the letter of revocation from the family.
On September 8, at 11 a.m. the Film Company sent the family a letter by overnight mail accepting the offer and they paid the requested fee. They also noted that they were accepted the offer within the 5 days provided to them by the family on September 5 upon which they relied.
On September 9, the family received the film company’s letter of acceptance but ignored it because they had already sent the letter of revocation.
The materials from the suitcase were included in the movie since the Director had assumed everything had been worked out. The family contacted me because they want to know their rights. Is there a valid contract to use the materials in the film? Can the family revoke its offer even though it was noted that the offer would remain open for seven (5) days? Is the film company liable for the actions of the Director by including the materials in the movie? Please explain your theories of liability.