Here are the children you've listed- William 1868, Ida 1870, Florence 1872, Lily 1876 and John 1878. Are there exact dates of birth in your grandmother's notes?
There is no birth registration for an Ida Smith anywhere in Ireland in 1870 (searched 1870-1879).
One registration for a Florence Smith in 1872 (Dublin North)- Florence Edith Smith.
Lily (no births for Lily Smith in 1876) could be a nickname for Elizabeth and William and John would bring up many possiblities.
Thanks aghadowey, Lily was Lady Lily Anderson CBE, wife of Sir Robert Anderson of Londonderry, Florence married a Mr Semple, Ida Isobel (aka Idabel) never married but lived with her sister Lily, and John's DOB was 9 September 1878, but I don't have much else. I will go through Grandma's notes again and talk again with my last auntie who met them whilst a child, and get back to you tomorrow.
Terry