There is one principle that is worth remembering. The LA cannot take into accounts assets not beneficially owned by the patient and not given away BY the patient to deprive themselves of assets.
Assuming they were tenants in common, Bill's mum only owned one half of the house. Bill's dad the other. Irrespective of when Bill's mum went into hospital, Bill's dad was the owner of half share and it passed to his executors upon his death. It matters not where Bill's mum lived and the SW is trying it on. Given that Bill's mum only owns one half, it is almost impossible to sell a half share of a house (see the CRAG guidance). If Bill were to sell the house, then mum's half share would be taken into account (although this sounds like an NHS funding case anyway).
I wouldn't worry about a solicitor unless the LA up the ante. The SW is wrong. They cannot argue that Bill or Bill's father have deprived themselves of assets since they are not the patient.
I accept that there is the possibility of a claim under the Inheritance (Provision for Family and Dependents) Act 1975 but view this as extremely unlikely. There are two practical points to be borne in mind. Firstly, claim has to be brought 6 months from Grant of Probate and secondly, I really can't see the Official Solicitor taking this one on. In the unlikely event that the Council have a LPA for mum, they would have to say that they would be responsible for her legal costs. I simply don't see that happening.