Normally, you would call the opposing counsel and request an agreed continuance pending a motion for a protective order. Pay a lawyer to help you.
[In accordance with the Avvo community guidelines, this communication does not constitute "legal advice", nor does it form an attorney-client relationship.]
I assume you are a party to the lawsuit and that you are representing yourself. A Motion to Quash that is timely filed automatically cancels the deposition until a hearing is held on the motion and the judge rules. If the motion to quash is overruled the judge can order you to pay costs, attorney fees, and possibly sanctions if the court determines that the motion was groundless. If you simply fail to show without filing a motion to quash then you are also subject to sanctions. You cannot file a motion to quash on behalf of your brother. That is practicing law without a license. It is a crime. You can represent yourself. You cannot represent someone else. You are in way over your head. Go get a lawyer.
DISCLAIMER: This is not specific legal advice and does not establish an attorney/client relationship.
Your question indicates that you may be getting into some real problems that come with trying to represent yourself. To answer your question specifically, the motion must be filed no later than the third business day after the notice was served or it does NOT stop the deposition from going forward. It also does not stop any deposition that the motion does not apply to. So if you filed only concerning your brother, then your deposition is still scheduled.
I want to emphasize that I am not giving you advice, because this question is so technical, that it can not be adequately answered on line. As someone else has said, you are in way over your head.
This is not legal advice. You should always discuss the specifics of your issue in person with an attorney. Be aware that there are time limits on all claims that depend on the kind of claim, so do not delay in seeking an attorney.