Find your support network

Just so you understand, your mother is a codependant to an abusive spouse, bottom line.  Though her status as a victim does not excuse her treatment of you and your sister, it is the direct reason - the two are separate and not to be confused.

The "playing favorites" game is typical within an abusive environment:  if you have ONE person that you can count on, that's saying something.  Again, this is inexcusable.

Finally, your mother is holding on to this man with a death-grip.  She is willing (as most abuse victims are) to sacrifice her own children to avoid being the focus of the abuser's control and wrath.

No, you are not crazy.  Yes, your eating disorder probably has everything to do with the dynamics of your family.  Yes, it would appropriate to look outside of your "family" to a network of friends that would be willing to help you get out of the poisonous environment.  You mentioned that you were in school - high school, or college?  If you're in HS, you can still finish out your year and focus on healing your Self, if you are able to find a safe environment.  Yes, you will have to take ownership of your Self and get involved in some abuse counseling, or involve yourself in an abuse support group.  Yes, you will have to be very, very proactive and understand, recognize, and accept that you will never, ever be able to gain your mother's approval as long as she remains a victim of abuse, herself !  I know it sounds insane, but abuse IS insane, and her disapproval of you has nothing, NOTHING, nothing to do with you, personally - it is just one of her coping techniques.  And, no, you are not responsible for creating this environment by anything that you believe you may have done - you are only responsible for your Self and your mother's angst, stepfather's tyranny, and sister's codependance are NOT your fault or responsibility.  You are only responsible for your Self!

Social Services will have a host of resources available to help you, as well as a great website:  www.stoptheviolence.com  and www.heartlessbitches.com.  That you can recognize that something is not right in your family is a huge leap toward your own healing!  And, you are of legal age and have the legal right to remove yourself from a dangerous, abusive environment and begin the healing process. 

Best wishes to you, my dear.  Things WILL get better if you make them so!