The birth records on the GRONI site for births of less than 100 years are not on-line. So the only child I can identify to this couple was Doris born 7.10.1913, registered in Antrim town. For births after that you would need to contact GRONI and get them to search.
I came across this probate abstract which may be Hannah. The full will is in PRONI and might be worth getting a sit should reveal additional members of the family:
Horner, Hannah of Bonita Rashee Road Ballyclare county Antrim widow died 18 February 1962 Probate Belfast 19 April to Margaret Elizabeth Mitchell married woman. Effects ?2747 0s. 2d.
The above lady was 79 when she died so that fits well with Hannah?s age in 1911
A George Horner died on 7th Match 1941 aged 27. Registered in Antrim. Possibly their son?
Couldn?t see George Horner senior?s death. Possibly he died away from the Ballyclare area.