Sorry, I have re-read your post and think I misunderstood. I assumed you meant your granddaughter had moved from the old address, where the DV took place, and now lived with you. That's why I refer to a change of address.
Upon re-reading, I think you're explaining that she still lives at the address near the school she's been allocated? Your daughter applied to schools near you instead, in the hope she'd get in, but she hasn't and has therefore been allocated a place at her nearest available school with places, ie her local school. Is that right?
I'm sorry, but your anger at admissions is completely misplaced. The circumstances are unfortunate but admissions have to do their job correctly. Their job is to allocate places, based on how well each applicant meets the criteria (based on home address). If your granddaughter is living with her mum still she is not a LAC (looked-after child). Her circumstances would not have allowed her special consideration. As 'disgusting' as that seems to you, those are the rules admissions are legally bound to follow. The schools your daughter applied to must be full, for her to have not been given a space. Your granddaughter's address means she sadly wasn't entitled to a place ahead of other children who applied. There's nothing admissions can do about that, regardless of what requests were apparently put in place. They can't allocate based on what individual sob-stories each family submits. I'm not calling your circumstances a sob-story by the way, I'm just explaining that that's not how it works. Otherwise people would make up all sorts of crap to try and get the schools they want (and sadly some do try). Your granddaughter's circumstances are unfortunate, but not something admissions would have legally been able to take into consideration. They've done nothing wrong.
You were hoping she would be given a school near you, to make her less traceable to her Dad. That hasn't happened, due to those schools being oversubscribed and her home address being too far away compared to other applicants. She didn't meet the criteria for any of the schools applied for, therefore she was given the local school by default as they still had places. Admissions can only work on listed preferences. There is no option of listing schools you definitely don't want under any circumstances. Your only way to state this is by rejecting the place which has now been offered.
You could try going on waiting lists for those schools she applied to, but I wouldn't hold out hope of her getting a space any time soon that way as there are bound to be others who live even closer who missed out (or move into the area afterwards and end up further to the top of list as a greater priority than your granddaughter, due to living closer to the school). Unfortunately, your granddaughter's current circumstances, awful as they are, would not give her priority over those who live closer.
Your best bet is to look at other options, which currently have spaces, in the area. Ones which your daughter can realistically get your grandchild to. I'm assuming she applied near to you in the hope you could help with childcare, as well as those schools being further away from the home address and therefore less traceable? Could you still support her with childcare from a school further away from you (if you drive? Obviously I'm not sure of your personal circumstances, but it could be an option if you do). Accept she may not end up in a school near you, but she could still get a place at one a safe distance enough away from the local school, maybe in the opposite direction?
Is there a court order in place? If there is, her Dad would not be able to collect her from any school, whether it's the local one or not. I'm just trying to reassure that she should still be safe in those circumstances, even if he knows what school she attends. If there's not a court order and he has parental responsibility it becomes trickier, as legally he could attempt to collect her from any school, whether that's the local one or any school in the area if he's managed to track down where she is. Again I'm not trying to scare you, it's just that forewarned is forearmed.
Look into other options. It's a very unfortunate situation, but admissions have done nothing wrong here.