Wonderful information, thank you so much! "... in 1863 the householder at No. 7 is Emanuel H. Orpen esq." Emanuel H. Orpen was the husband of John Bateman's sister, Letitia, and so an uncle of Jane Bateman. Presumably Jane was staying with her aunt and uncle at that address.
I think the family home in the 1820's might have been on Merrion Square, but I don't have an address to be more specific.