You can apply for an L-2 visa stamp in India. While outside the US you have no immigration status and there is therefore nothing to extend.
J Charles Ferrari Eng & Nishimura 213.622.2255 The statement above is general in nature and does not constitute legal advice, as not all the facts are known. You should retain an attorney to review all the facts specific to your case in order to receive advise specific to your case. The statement above does not create an attorney/client relationship. Answers on Avvo can only be general ones, as specific answers would require knowledge of all the facts. As such, they may or may not apply to the question.
I agree with Charles that the proper step, if you must travel to India, would be to apply for a new L-2 visa stamp at the nearest U.S. embassy. Even if your husband filed for an extension of your L-2 visa while you're still here, it would be abandoned the moment you left. That would be a waste of time and money.
You may be worried about "administrative processing," meaning you might be stuck in India waiting for your visa stamping to be approved. This is always a possibility, especially in India. You should make sure that your husband's visa is in order, that his company is valid, and that everything in his L-1A application is true and correct. If not, indeed you could get stuck. I have seen instances where the Embassy seems to be skeptical about the spouse's visa (often an H-1B where they are working on contract), and it sure feels like they are trying to apply pressure on the spouse to return for a review of their visa, too. If this happens, I would certainly get your husband's company and local congressperson(s) involved. That has been successful for us and our clients in the past.
I also noticed you are leaving to give birth to your baby in India. That's unusual. Why wouldn't you want to have the child in the United States?
In any event, since you're traveling, and this is really important, don't trust everything you read on the internet. Your research will certainly turn up conflicting advice, some of it probably good, most of it probably worthless or dangerous. You and your husband should consult with a good immigration attorney in your area. By doing so, instead of speaking to the company's immigration attorney, you ensure that what you discuss is confidential. And an attorney whose only duty is to you may give you advice that is in your best long-term interest, rather in the company's best interest. Our firm (www.hvlawgroup.com) has a Wilmington, DE as well as a Philadelphia office. Feel free to come see us if you have any questions.
(610) 664-6271. John Vandenberg focuses his practice solely on immigration law. You can keep up to date on immigration law by liking the firm on Facebook at www.facebook.com/hvlawgroup. His response to your question is general in nature, as not all the facts are known to him, and does not constitute legal advice. Retain an attorney experienced in immigration law to review all the facts in your case in order to receive advice specific to your case, since that protects both you and the attorney. Mr. Vandenberg's statement above does not create an attorney/client relationship.