I think I may have found Annie's family BUT it's somewhat complicated to try and explain but I will do my best (2 pages of notes to decipher). I believe that she was somewhat older than she admitted on 1901/1911 Irish census (in which you've already pointed out was 36 in 1901 and 39 in 1911!!!
I believe she was actually born at the end of 1857 but to prove would necessitate getting at least a couple of certificates.
1861 Census - Brace Meole & Nobold, Shropshire (Shrewsbury regn. district) ref. RG9-1874-123-10
Richard Bevan 44 Ag Lab born Condover, Shropshire
Mary (?) 47 born Newtown, Montgomeryshire
Sarah Ann 3 born Brace Meole, Shropshire
(I believe Mary is an error and should read Elizabeth so please bear with me).
1851 - Nobold, Shropshire - ref. HO107 - 1992 - 749 - 3
Richard Bevan 33 Ag Lab born Meole Brace, Shropshire
Elizabeth Bevan 37 born Montgomeryshire, Wales
Mary Thomas 20 Visitor House Serv. born Montgomeryshire
Jane E. Bevan 7 born Meole Brace, Shropshire
(his father living 3 doors away).
Daughter Jane Elizabeth Bevan bp.20/7/1843 Meole Brace, Shropshire dau. of Richard/Elizabeth (can 't find actual birth entry).
In 1861 Jane - 18 - working as a Nurse in a Lunatic Asylum in Shrewsbury.
Now to Sarah Ann Bevan - her birth reg'd as Sarah Ann Beavan Dec.qtr.1857 Shrewsbury - baptised as Ann Sarah Beavan 27/12/1857 Meole Brace, dau. of Richard and Elizabeth.
By 1861, as you can see on census, she is Sarah Ann again.
Father Richard Bevan dies in 1870 and bur.10/3/1870 Meole Brace - in 1871 it looks like widow Elizabeth Bevan is working as a House Keeper in Shrewsbury and daughter now Ann, b13, (recorded as Beaven) working as a servant in Pontesbury, Shropshire (shown as born Nobold - Meole Brace/Brace Meole often shown 'with Nobold'.
Can find no trace of Sarah Ann/Ann Sarah/Ann after 1871!!
Found an online tree which contained little just that Richard Bevan and Elizabeth Jones had dau. Jane Elizabeth. No marriage. (also a few other trees that show Jane Elizabeth belonging to a John Richard Bevan and Elizabeth Christina Jones - again, no marriage just a circa date and no sources!
However, I believe I could have found the marriage but this would need checking out:
Richard Brown of Meole Brace, son of Richard Brown, and Elizabeth Jones, of Shrewsbury, dau. of Luke Jones, married 24/1/1843 Meole Brace, Shropshire.
I think that 'Brown' has been misread for Bevan - other findings indicate that Richard Bevan was indeed the son of a Richard Bevan who lived in the same place.
Richard Bevan married Elizabeth Green 1816 Gt. Harwood, Shropshire (familysearch but with no further details) children:
William bp.17/5/1816 Harwood, Shropshire, son of Richard and Elizabeth
Richard bp.6/7/1817 ditto
Jane bp.28/2/1819 Meole Brace, Shropshire, dau. of Richard and Elizabeth
Anne bp.1/4/1824 Meole Brace ditto
John bp.8/7/1827 Meole Brace, son ditto
In 1841 Richard senior and wife are living with Elizabeth 20 and Harriet 10 but haven't found baptisms for these 2. Son Richard is living in the household next door.
To hopefully prove this scenario, you will need (1) birth certificate of Sarah Ann (Ann Sarah or Ann) Beavan Dec.qtr.1857 (baptised 27/12/1857 Meole Brace) to confirm mothers maiden name is Jones and (2) marriage certificate (or check made with original parish record) to confirm that the marriage for Richard 'Brown' and Elizabeth Jones in 1843 is actually Bevan not Brown.
Annette