not sure what Wicklow details you are looking for, but Annamoe is located on the road between Laragh and Roundwood and appears to be in the Civil parish of Derrylossary and the RC parish of Glendalough. You dont mention the familiy religion but Catholic records for this parish survive back to about 1807 with several gaps around the late 1830s, Church of Ireland for Derrylossary have not survived. The RC records are available on microfilm in the National Library. The Irish Family History Foundation (
www.irish-roots.ie) also have many RC baptism transcripts for Co. Wicklow.
I also dont see any promising marriage matches for the marriage of John & Catherine on the
Irish Civil Index, so it's possible they married before 1864.
Details for both Thomas and Lawrence are on the IGI, and both include references to help locate civil details for them. The IGI does not show a birth for John using a parent search in Ireland or England, but this does not include all births. The Registration district for the Annamoe area is Rathdrum and there are a few John Kavanagh births in that district in the 1860s, but the only way to confirm if any of these if part of the family would be to order birth certs for them
Shane