Technically, your aunt could file a custody action against you, but she would have a very hard time being successful. If this were an action between parents, then the court would consider each parent having equal rights to custody of the child. However, since she is a third party to the child (not a parent), she would have a higher standard to overcome to obtain custody from a parent.
This response is being given based only on the facts presented in your question. Additional facts may significantly change this response. This response is not intended to be legal advice and shall not in any way establish an attorney-client relationship.
She could file for custody. However there would be a significant number of hoops to be jumped through in orde for her to obtain custody based on the provided information.
Based on what you wrote, it sounds like you and your husband are good parents even if your aunt disagrees with your parenting styles. That is not enough for her to have custody of your daughter. A relative having custody usually comes about because both parents are unable or unfit to care for the child. From what you have said, both you and your husband are involved and there is nothing to say that you are unfit.
If she were to file for custody, there would have to a hearing before a Judge to determine whether she should have custody. (You can agree to her having custody but that does not sound like what you would be willing to do.)
It would take unusual facts for an aunt to take a child away from parents, so I don't think you should worry unless she files something. Obviously if she does, hire counsel at that time.
If you find this answer helpful, please mark it here on AVVO as helpful. In answering you, I am attempting to communicate general legal information and am not representing you (and am not your lawyer). Do feel free to call me at 404-768-3509 if you wish to discuss actual representation (the phone call also does not retain counsel; that requires an office visit and appropriate paperwork). In that a forum such as this provides me with limited details and doesn't allow me to review details and documents, it is possible that answers here, while meant to be helpful, may in some cases not be complete or accurate, and I highly recommend that you retain legal counsel rather than rely on the answers here. (You can also email my office at email@example.com . An email also does not retain my office, but can help you get an appointment set if you prefer not to call). I am happy to discuss possible representation with you. Any information in this communication is for discussion purposes only, and is not offered as legal advice. There is no right to rely on the information contained in this communication and no attorney-client relationship is formed. Nothing in my answer should be considered as tax-advice. To ensure compliance with IRS Circular 230, any U.S. federal tax advice provided in this communication is not intended or written to be used, and it cannot be used by the recipient or any other taxpayer (i) for the purpose of avoiding tax penalties that may be imposed on the recipient or any other taxpayer, or (ii) in promoting, marketing or recommending to another party a partnership or other entity, investment plan, arrangement or other transaction addressed herein. I am also required to advise you, if your question concerns bankruptcy, that the U.S. Congress has designated Ashman Law Office as a debt relief agency that can help people file bankruptcy.
Sign up to receive a 3-part series of useful information and advice about child custody law.