The LA can look back at any transaction to deprive a resident of capital. If a "significant" reason is to avoid liability for a contribution to care home fees, they can deem that she has notional capital to the value of the asset given away which they will normally seek to reclaim by way of a deferred charge on the property.
However, their CRAG guidance considers that it would be unreasonable to assume a young person with no foreseeability of residential care gives away assets with a view to avoiding care home fees.
The LA can also disregard property if a dependant relative under 16 or a carer is living in it (say for instance if a person gave up their home to live with your mother and care for her and then remained there when she went into long term residential care).
Other than that, it is actually extremely hard to avoid paying for care. She needs to bear in mind that if she successfully gives capital away (a discretionary trust perhaps), that LA care is not of a high standard and often results in minimum facilities and a shared room. There have been no decided cases on this area of the law, so it is difficult to say what would and would not be successful. The only thing that might be successful is a Deed of Variation of your father's will (if within 2 years of his death), since the variation is read back into the Will as if it is done by your father, rather than by your mother. That is the case for tax law, but has not been tested elsewhere.