Before I say anything else, I want to agree with Other One about the dangers of hypnosis. There are good people that use this technique to simply try to get at the truth, and there are others who create false memories. Your child could actually start believing she was abused when she was not as a result.
Based on what you have said, my guess is that your daughter is probably attending public school. Am I right so far? Someone likely saw something in her behavior that caused them to think she had been abused. The first person they blamed was your husband and then they thought that if it was not him, it might be your Father-in-law. I am guessing they are going on behavior rather than actual claims by her that she was abused. They are seeing something that has led them to these conclusions.
If your husband has done nothing wrong, and even the state officials aren't sure he did anything wrong, leaving him won't fix anything. I think what I would do is continue to fight this through the legal system, but rather than just figuring within yourself that the abuse charges are nonsense, and scoffing at them, try to find out exactly why anyone suspects abuse. Something had to happen. If you can figure that out, you can trace the behavior to the cause. It may be that your daughter suffered abuse at the hands of an outsider. It may be that she was influenced by something she saw that caused people to suspect abuse. It may be that someone who doesn't like you falsely accused you. There is just not enough information here to make any judgments about this, but I believe you when you say there was no abuse taking place in your household.
I wish you the best and pray that God will reveal what is going on to you so you can act accordingly. I pray that you will get your daughter back with your family in tact. Just don't do anything in haste, and try not to despair. I have no idea why you are going through this trial, but as bad as this nation has become with it's overreach by the government in interfering with how children are raised, most of the time, when something like this happens, it is based on an anonymous tip or some sort of behavioral change someone saw. If you can get to the bottom of it, your chances of success in getting your daughter back should increase. I am really sorry this has happened to you. I can see why you have been so upset lately. I had no idea it was something on this level. Just don't give up. As bad as things seem, they are not hopeless.