The answer here is “yes, you can bring your own sign language interpreter.” You can bring someone with you as your companion or interpreter but you would have to buy two tickets.
BUT the requirement for effective communication does not require the theater to take any action that would cause a fundamental alteration in the goods or services being offered. Having someone sit in the seat in front of you so she could interpret would disturb the other patrons and would fundamentally alter the experience for them.
The requirement to provide effective communication includes the obligation to provide effective communication to companions who are Deaf. So the hospital is required to find a way to communicate with someone who has a communication disability “as effectively” as they would communicate with that person if he/she did not have the disability.
For example, suppose a school system employs an interpreter to work with a Deaf child in a classroom. Now suppose that she is asked by her Principal to interpret for a Deaf parent during an appointment where the parent is very upset about an issue. Imagine that the parent proceeds to cuss out the Principal. How difficult that scenario might be for the interpreter. She doesn’t want to jeopardize her job by saying all those things to the Principal. But if she doesn’t – if she “sugar coats it” – that is unfair to both sides.
State and local governments must give primary consideration to what the person with a disability requests. So if this same person who is Deaf plans to attend a City Council meeting and requests an interpreter, the city must provide it unless doing that would somehow be impossible - maybe because the request was just made the morning of the meeting and no interpreter could be found on such short notice. However, the city must make a good faith effort to secure the services of an interpreter.
The ADA regulations also say that a public entity or private business shall not rely on an accompanying adult except: "where the individual with a disability specifically requests that the accompanying adult interpret or facilitate communication, the accompanying adult agrees…and reliance on that adult is appropriate under the circumstances."
Title II and III ADA regulations specifically state that you cannot be required to bring a family member or another individual with you to interpret. Instead the doctor is required to provide auxiliary aids or services in order to ensure effective communication. This could mean hiring a qualified sign language interpreter or it might be another method, such as video remote translating—as long as the communication is equally effective for both of you to understand each other.
A public entity or private business conducting a workshop cannot require an individual with a disability to bring another individual to interpret for him or her.