Have you searched for the wife in the 1911 census? People in institutions should be listed by initials (for example, Mary Ryan listed as M. R.) so you might find her in the asylum at that time (might also explain why husband said he was a widower).
Not sure I understand this bit "What would the likelihood be that a child was committed to the Ballinasloe Lunatic Asylum?" Do you mean that you think a child of the couple was in the Asylum?
People were institutionalised for all sorts of conditions that were misunderstood or untreatable. Epilespy, autism, deafness, blindess, etc. are all possibilities.