If the head of a family is a veteran, as defined in s. 45.01 (12), or a person under s. 45.51 (2) (a) 2., and is hospitalized or institutionalized because of disabilities in a county other than that of his or her residence or settlement at time of admission, aid shall be granted to the dependent children of the veteran by the county wherein the head of the family had his or her residence or settlement at the time of admission so long as he or she remains hospitalized or institutionalized.