This appears to be the house shown as Valetta House which was on the site now occupied by the multi-storey carpark behind the library on Library Road. The second house is probably a gate lodge or annexe to the main house.
At the time of Griffiths Valuation (1849) Valetta House was occupied by Major Edward W Drew, and Drew is also recorded there in the Topographical Dictionary of Ireland 1837
The censuses of 1911 and 1901 both show a large house and a smaller house on Valetta Avenue. The larger house (14 rooms) is occupied by the Browett family. Francis Browett had shops at both 7 and 19 Upr Georges St, selling ironmongery, and had a nursery and fruit business. He traded as E Browett & Co