Other possible scenarios:
They buy the house from mother , raise a mortgage, pay the CGT.
Mother sells house, pays CGT and gifts balance of money to offspring to buy own property.
Mother raises mortgage on property ( subject to her own financial circumstances) and keeps property in her sole name and they rent it from her. When she dies, offspring get property with no CGT payable.
They rent the property and raise a personal loan to do renovations.
What they are proposing is , essentially, the best of all possible worlds, which is unlikely to work in practice.
mf