Hmm, I don't think the LDS is always right, some days you will get one answer and another on a future search.
Perhaps your next step is a copy of a birth certificate from the General Registry www.groireland.ie
You have good dates, and both parents. Look to see what their criteria are for getting records. You also have the registration #'s on a couple of the children which will help them find something.
The other before you spend money at the General Registry is to phone and see if the Latter Day Saints have the microfilm or if it needs to be ordered. This maybe a less expensive way of doing things. Here is the list again:
Timothy 24 April, 1867 (#?)Sneem, FHL Film #101149 (Cathrine)
Patrick 14 Mar 1869, #350 Sneem, Registration No. for GRO LDS#101184 (Kate)
Mary 17 Apr 1871 #372, Sneem, LDS#255824 (Catherine)
*Bridget 3 Sept 1873 (#?) Sneem, LDS#255887 (Catherine)
*Bridget 30 Jan 1874, Emlagh, LDS 255898 (Kate)
Daniel 14 Dec 1875, (#0279) Sneem LDS 255943 (Catherine)
It could be possible for the LDS to be incorrect when *these were transcribed? I would then go with the 1873.