Hi,
The entry in the death record certainly seems to be her. I can't make out the word after 'widow'. I would be very interested to know what others think is says.
I don't think that your explanation for the children missing from Burke's Irish Family Records can be right. The petition that you found clearly stated that the three children were minors when their father died, which was in 1814. They must therefore all have been born after 1793, ie after all the children listed in Burke. Their parents married in 1783.
The author of the Burke genealogy plainly didn't know when Louisa nee Sandford died, so it is possible that she died before her husband, that he married again and that the children were from a second marriage. However, it is not clear why this should have affected their inheritance of the Coolmore estate which came from their father's rather than their mother's family.
Alan