Oh, so sorry to hear this.
But your daughter is in the safe place. I understand you are scared and freaked out, but first thing to do is forget One Flew Over the Cuckoo's Nest and all the other popular culture psychiatric wards and asylums. Nowadays psychiatric wards are hospitals like any other hospitals. Bad food, noisy, often feel too cold, have crappy coffee, ugly colour schemes, staff that may be busy and seem bit abrupt or rude at times, you never feel you get enough information or they are talking gibberish or simply can't say anything definite. In other words they have all the makings of crabby hospital experience (if you don't get lucky), but that is it. They are no horror houses. Unpleasant at worst but can also surprise and be more pleasant experiences.
Try not to worry for your disability. I'm of course not from USA but simple logic says, that you are certainly not an only one whose disgruntled child, parent, ex-spouse, neighbour, new spouse's ex etc. has made bogus accusations against them. Dealing with them is likely total routine to officials and giving the circumstances I doubt you daughter has been able to write an email that would even be believable. And even if it was, I'm sure they actually need some proof to do anything to you.
Try to take this time she is in hospital as a breather from your situation. And if possible, try to find out what services hospital may have for discharged patients. Your living situation is toxic for both you and your daughter, this could actually provide you some assistance with getting rid of you too living together.