She has now been told that she can’t take the time off. If she does she will be moved onto a stage 3 and dismissed.
The standards are 2 absences or 10 days in the next 6 months of them issuing a stage 2.
Seems this manager is another one of the threating types.
Also your manager should not be telling your friend to offer a cash payment to cover for leave.
As your friend is the primary carer for her mum and this is a family wedding then you could put in a grievance and point out that your friend has days owing to her and that as her mum is dependant on her help then Royal Mail are discriminating against her and her mum under the Equality Act(Discrimination by association.)
What's the rep doing about it?