You need to consult a qualified immigration attorney for guidance. You can file a petition for your mother, but based on the facts you have provided, she will need a waiver for her unlawful presence. Moreover, she may hae triggered a permanent 10 year ban that is not waivable depending on the specific facts surrounding her first entry you mentioned (and if there have been other entries). She will not have a qualifying relative for waiver purposes for the unlawful presence unless she has a U.S. citizen or permanent resident spouse or parent (her children will not qualify). The bottom line is, there are too many variables to try and meaningfully answer your question. Only after thoroughly discussing the specific facts and circumstances of your mother's case would an immigration attorney be able to advise you if and how best to proceed. You can search for an immigration lawyer at www.ailalawyer.org. Best of luck to you.
You will certainly want to contact an experienced immigration and find out the exact circumstances of your mother's detention at the border. There is a way to request this information from the authorities, if she was in fact fingerprinted. There may be possibilities for a waiver of inadmissibility, however it would be impossible to make an informed comment without looking into her full immigration file. Best of luck!
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By seeking a consultation with a qualified and experienced immigration lawyer in your area.
Behar Intl. Counsel 619.234.5962 Kindly be advised that the answer above is only general in nature cannot be construed as legal advice, given that not enough facts are known. It is your responsibility to retain a lawyer to analyze the facts specific to your particular situation in order to give you specific advice. Specific answers will require cognizance of all pertinent facts about your case. Any answers offered on Avvo are of a general nature only, and are not meant to create an attorney-client relationship.
From just the little bit you've shared already, there are a LOT of things to consider and my colleagues are correct that working with an immigration attorney will be necessary. None of considerations that need to be examined and investigated should be handled in this forum; it's not confidential and you need to be able to share everything - the good, the bad and the ugly - with someone to get a responsible answer.
If you'd like, let's get together to talk through what may and may not be available to her. You can contact me offline to schedule an appointment for a full consultation or over the phone for a brief chat.