It is always hard when we are watching someone we love get pulled down or used. Unfortunately, you cannot control your mom or force her to see that she isn't helping your cousin. All you can control is what you allow to affect you and what you are willing to be part of.
You said that you have gone out with your mom and talked to her without your cousin being part of the conversation. Have you thought about making a boundary with our mom that you do not want to hear any news about your cousin, that you do not want to see your cousin if you are coming to pick up or visit your mom, and that you are not willing to get involved with anything pertaining to your cousin? This way you can continue to have a relationship with your mom but not have to add your cousin into it. Will it make you worry less about your mom or make you less angry about how your cousin in using her? No, but unfortunately we can not control others or force others to agree with us so we have to accept certain things and continue to move on.
Is your mom willing to see a counselor, read some literature on codependency and addiction, or even just go to a support group? Some people really break away from the addict when they become more informed, that will only happen if she is willing to open her mind, take in all the information, process it, and then apply it to her life.
I hope things start to improve for your family. I know how hurtful and frustrating this can all be.