Yes, I've been thinking the same, that it was Kate who was 9 when Lucy died.
Kate is 1 week old in March 1902 but there doesn't appear to be a birth cert so it doesn't look like she was born in the workhouse, I think it's going to be the same for the rest of the children, the only one with a cert it seems is Lucy's death cert but the children would have been baptised.
You would need to look through the registers more carefully but first pass it looks like Mary brought her children to the workhouse for short spells in the winter, I think the man John was with them and may even be the children's father.
There just doesn't appear to be any other combination of Kate and Lucy any where in Wicklow so I'd say these are your family. The death of Lucy would I'd say confirm it.
Michael on Kate's marriage cert could be made up, it wasn't uncommon to make up a father or he could be a father figure from some point in her life.
We haven't found any connection to Tinahely but again it may be some where she lived at some point.
If her brother John attacked her it might explain why she never mentioned having brothers.