So the lady is normally volatile, and abusive to your family in your home----may I ask why you are bothering with all this.Time is of the essence I realise for the property , but why not let her calm down a little before you try to help again.
If she is delusional and may have a serious mental problem , as you suspect from your experience , it is unlikely that she will react in a favourable way if pressurised and harried about her housing intentions.
A very low key approach to her problem may help her.After all the problem is hers ,not yours, inspite of her being part of your family.
I am not sure that you can pull out ater contracts have been exchanged, but do not have knowledge on this to adviise.