Thanks aghadowey,
Here's what I've gathered so far (mostly from
http://freepages.genealogy.rootsweb.ancestry.com/~rosdavies/SURNAMES/G/GilmoreGilmer.htm, Family Search, the Washington State digital archives, and family records)
Joesph Gilmore (b. ~1810???) Don't know much else about him.
William Gilmore (b. 1836, d. 1911 in Seattle); Parish Killyleagh; husband of Margaret McDowell ; father of Pendelina b. 30 Jun 1868 & Robert McDowell Gilmore b. 10 Mar 1874
Margaret Gerch McDowell (b.1843, d. 1903 in Seattle) Parish Comber; daughter of Robert McDowell ; married William Gilmore 26 Dec 1862
Pendelina Gilmore (b. 1868, d. 1947 in Seattle) daughter of William Gilmore and Margaret Gilmore
Thanks in advance for any help.