Abs no expert on this but I believe whether your Mum has capacity or not I'm pretty sure that she can't 'gift' that much money to either you or your sister. There is an annual limit and that's if you don't pass away within 7yrs of gifting it.
This seems to be some sort of inheritance tax rule snippets muddled up but is certainly in no way correct. There is nothing to prevent anyone with full capacity who has surplus capital (ie no deprivation of assets issues) from giving as much as they want to anyone else eg if you have £10million and wish to gift £1million cash no issue. The issues that might arise are related to tax. The 7 year rule applies to gifts made above the annual limit, although the application of this is not as straight forward as it first appears.
If cash is given the only tax in play is inheritance tax, if other assets are gifted than capital gains tax, settlement rules and inheritance tax all needed to be considered, and depending on the nature of the asset SDLT for land/property and stamp duty reserve tax for shares. There are a whole host of exemptions but these rules are very complex and professional advice from a suitably qualified tax practitioner should be sought if these sort of gifts are contemplated.
As
@nitram points out, IHT only needs to be considered if the estate will be above the IHT threshold at death, otherwise there is no need to worry about lifetime gifts within 7 years. As well as the £325k annual limit there is also an additional sum on sale of a property - with a few anti avoidance rules around it. Much of tax legislation contains the initial rules which might be say a paragraph and then follows several pages of anti avoidance catches to rule out those trying to find ways round.
If a cash gift is made out of income that is surplus to annual living costs then this is not subject to inheritance tax or any other tax, I've seen annual gifts of £30k upwards out of income - letters were written to confirm out of surplus income.
There are a lot of complex
tax rules around gifts but nothing in them to prevent gifts being made.