Hello Ruth
I don't follow sibling's children usually.
All I have on Gilbert Hayhurst Park is that in the 1901 Census a Gilbert M Park age 32 (b. 1869, Kendal), married, is cook & steward on the SS Grampus (registered Glasgow). I think this is Gilbert Hayhurst even though it is M on the image.
I have found a marriage for him to Mary Elizabeth Hall, Dec qt 1892, St Michael and All Angels, Wigan
and that is it. No death, no wife or him in 1911, no wife in 1901