In California, there are no hard and fast rules about who cannot attend a deposition. In short, unless you can make a sufficient argument for protective order to exclude a witness, let them in.
In any event, any named party is allowed to be present, as well as a representative of any entity defendants. You will lose a motion for protective order every time on these. Husbands, wives, significant others of the deponent are not out of the question.
If any of the attendees become disruptive you have the right to end the deposition and seek a protective order on the basis of the conduct you are seeing. Be sure to make a good record of the bad conduct. In other words, give plenty of warnings before you pull the plug.
Good luck to you.
This answer should not be construed to create any attorney-client relationship. Such a relationship can be formed only through the mutual execution of an attorney-client agreement. The answer given is based on the extremely limited facts provided and the proper course of action might change significantly with the introduction of other facts. All who read this answer should not rely on the answer to govern their conduct. Please seek the advice of competent counsel after disclosing all facts to that attorney. This answer is intended for California residents only. The answering party is only licensed to practice in the State of California.