DD was impossible to settle in preschool at 2.5yo. After 3 weeks of gradual withdrawal, and her screaming solidly to the point where I had to go back and pick her up, I withdrew her.
I tried again with school Nursery at 3.5yo. She still wasn't ready. It wasn't until she was 4yo that she was ready to be left like that.
DS1, on the other hand, started Nursery at 4mo, and was out if my arms and crawling towards the toys before I had even got his coat off.
DS2 was not able to settle at 2.5, besides which he was not walking and non verbal at that age. However, at 3.5, he enjoyed Nursery after a week of settling.
Each child is ready at different times. I think it would have helped me with DD if I had been more confident in my own belief that she wasn't ready. It was only when one mum took me to one side, and told me that I didn't have to send her if she wasn't ready that I realised the preschool staff weren't necessarily saying what was right for MY DD.
Maybe just gently tell this mum that she doesn't HAVE to send her DC to Nursery yet if HER DC isn't ready to be left like that yet. She may not realise that not every child will be ready at the same age. She may just look at it that 'all' children start preschool or Nursery by 2.5, so that's what happens, and the staff are right and her DD will get used to it.
A quick pointer that she knows her DD best, and can decide herself if her DD is ready to be left or not might actually really help. It helped me.
I didn't know when I had my DD that some DC's just weren't ready to be left at 2.5, and that though they may settle eventually, if you think it is too distressing for your DC, you CAN take them out and try again 6 months to a year later, and if you think another setting would work better for YOUR DC, you don't have to stick with your initial first choice.
A word in her ear may help her to decide whether her DD being in Nursery NOW is worth the distress it is causing her DD...