As for unemployment, most agencies have you sign a clause saying that due to the variable nature of home care, they can't guarantee hours. You are still employed.
These are the reasons I've gotten when I'm asked to remove a nurse from a case: She is always 5-10 minutes late, she talks too much about her personal problems, she signed that she did ROM exercises but I was watching from the kitchen and she never did, I had to stop back at the house to pick up my cell phone and she was brushing my daughter's teeth while she was reclined in the bathtub and wet/cold, she has a bad attitude, she was on her cell phone arguing with her husband all morning, she texts all the time, she was on the internet looking for a new car all day (some of these were reported to the parent by the child that was being cared for... some nurses forget that because a child is disabled, some can still communicate) She never cleans up after herself. These are just the few I can remember at the moment.
In almost every case it is because the professional boundaries have been repeatedly crossed moving that 'line' back further and further until either the caregiver or the family becomes uncomfortable. I can usually review our 'code of ethics' and show the nurse exactly where the problem began to occur. It's a very fine balance of keeping it professional yet not treating a family like their home is a hospital and the nurse knows more than the parent. There are also times when there is no good reason given. It's never easy to find you aren't wanted back but try to learn from the situation and move on.