The larger home is one of the safe and reasonable options surely marshy36, unless there’s evidence that it provides an unsafe standard of care? It will be regularly inspected by the Council, and the Healthcare Inspectorate so you could look up reports.
The best I think you’ll be able to expect if you can produce concrete evidence that the larger home can’t meet your mum’s needs is that the Council will find another one that doesn’t have top up fees which does meet them. My previous role was NHS, but was heavily involved in complex placement cases, and I’ve never known a case where a family was able to successfully argue that the council had to pay top up fees to place their family member in their home of choice. The only circumstances when they paid top up fees was if the person’s needs were so complex that they needed a specialist placement, falls would not fall in that category. Hopefully somebody who has recently worked in the field for a Council will be able to advise you.