I'm sorry to hear about your difficulty here. Generally, I would say that she does have a responsibility to care and house you during her custodial time, but holding her accountable for this may prove to be more difficult. Normally, I would suggest that you simply go home to your dad and have him petition the court to remove your mother's custodial time, since she clearly doesn't want to exercise it. However, you have to understand that you are the minor child in this case, and while the court will listen to your desires as a 16 year old (rather than a younger child), the court really only has jurisdiction over your parents in settling visitation matters. Of course, if your situation is unbearable or abusive at both parents homes and nobody wants you around, you could seek to have yourself emancipated and you will be authorized legally to make your own decisions. Of course, that would release your parents from their obligations to you for the next 2-3 years, which probably isn't advisable unless you are being abused. I suggest you go back to your dad and just try and work things out with your mom later, if possible. Otherwise, you might speak with an attorney in your area about help if neither of your parents cooperate in resolving this.
Attorney answers to questions are for general purposes only and do not establish an attorney-client relationship. This answer is meant for informational purposes only and should not be construed as legal advice within the bounds of a professional relationship. It is always best to seek counsel with a competent attorney experienced in your area of issue and fully informed about the facts of your case.