You absolutely need to consult with an attorney. Analyzing immigration consequences of criminal convictions is nearly impossible without seeing the record of conviction. The DUIs should not be a bar to adjustment (but it depends on state law). It can definitely be a bar to good moral character, however. Also, the manner of entry will be critical to your case. If you are ineligible to get your green card in the United States you can try consular processing, but you may require waivers. The battery can also be a problem, depending on the language of a the criminal statute. You really need a lawyer to help you navigate these issues. Seems like you have possibilities (I am assuming your daughter and maybe your wife are United States citizens) but you need some good legal advice. Good luck!
You need to retain an experienced immigration lawyer, whether myself or one of my colleagues, to review all the facts, advise you, and handle the case.
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.