OK, it sounds like it is an emergency placement when someone has to go somewhere that has a space. The best homes usually have a waiting list. The other possibility is - was she sectioned because of her aggression? If so, is she in an assessment unit to try and sort her out with medication? If she is in an assessment unit you will have a very limited choice about where she could go and you may not be able to move her at all.
Assuming that she hasnt been sectioned, if you want to change care homes the funding is fairly important. If your nan is self-funding - ie paying for the care home from her own savings or money from the sale of a house, then you can just find somewhere else that would accept her (not all of them will if she has aggression) and move her, but you will have to do all the work of finding somewhere yourself.
If she does not have the funding to pay for the care home herself and the Local Authority are paying at least part of the fees then you will have to work with the Social Worker. Her social worker should be able to give you a list of other places, but beware that the family may have to pay top-up fees, which can sometimes be quite a lot and will inevitably go up as the dementia increases, so family must be careful not to take too much on. Im sure your parents will already know about this..