You are not clear about the specifics of the battery charge however I can tell you that the false imprisonment is a serious offense. It is usually accompanied by a charge of kidnapping, as well.
Under NM law you can be imprisoned for your first offense of this nature. If you are employed or in school, have a steady residence, are not a danger to the general public and/or a risk of flight, then you are a good candidate for a probationary sentence.
You need to get a good attorney. Due to the nature of these domestic violence charges, they are often ver defenseable.
My comments are not intended to establish an attorney-client relationship, are not confidential, and are not intended to constitute legal advice. Proper legal advice can only be given by an attorney who agrees to represent you, who reviews the facts of your specific case, who does not have a conflict of interest preventing the representation, and who is licensed to practice in the appropriate jurisdiction where the legal issue may be filed, and who is licensed as an attorney in the state where the law applies.