I know the amount she's paying will be based on a purchase of 225,000, but I think it is possible that the RATE that she pays is based on the total value of the house, 450,000.
FTB rate for 450,000 = 6%
50% of this rate due to consanguinuity = 3%
3% of 225,000 = 6,750
This would mean that she pays the same total stamp duty as if she bought the whole house herself as a FTB, except that she's paying it in two halves. Logically this would make sense, as otherwise people could break a transaction down into incremental purchases of under 100k purely to avoid SD.
Obviously, you should get revenue clarification / profesional advice on this.