How do I find out about the Chorlton Union School which I assume is part of the workhouse and if and when people were admitted and discharged?

I have a family who in the 1881 Census lived in 4 Porter Street, Ridgeway St, Manchester
Father: Thomas Horsfield b:abt 1854, Oldham, Lancs. Packer, Cotton Manufacturing.
Mother: Selina b: abt 1853, Manchester. Lancs
Children: Elizabeth E b: abt 1873, Manchester. Lancs.Scholar
Hannah b: abt 1876, Manchester. Lancs. Scholar
Thomas b: abt 1879, Manchester. Lancs
Martha A b: abt 1880, Manchester. Lancs

Then there is the birth of another child Births Dec qtr 1882 - Horsfield Joshua

Then the head of the house (Thomas) dies in Sept qtr 1886 at age 33

In the 1891 census Thomas and Joshua are in the Chorlton Union school and the rest of the family are split up elsewhere, Selina having remarried.

Were they all admitted to the workhouse and then got out individually?

Thanks for your help,
Bev