Wow, this family really misled you! I would definitely talk to the parents about this, but make sure it's not around the children. If the kids overhear you, they may take it to heart and feel that they aren't loved or they are bad children, etc.
When you talk to the parents, tell them that they told you that you only had to do certain things, but over time your responsibilities within the family grew and grew. If its a raise that you want, then tell them that you would like more money because you are doing beyond what was expected from you from day one.
Also, you need to think about if the situation is worth it. It sounds like the family is trying to "guilt" you into staying- saying that no nanny has ever stayed for the children because of their disabilities, etc. It sounds like they are trying to take advantage of you by saying the things they do and adding so many duties to your job without even a single thought of raising your pay. I'm sorry you have to deal with all of this, and I wish you the best of luck!