In Nebraska, a child is presumed to be emancipated when he moves to his own residence. However, that presumption can be rebutted by a showing that the child is not capable of supporting himself financially and managing his own affairs. Further, if one of the parents objects to it, the court cannot generally order it.
So, this brings us to your next question. Under NB law the money that you pay in support, is by statute, deemed the personal property of the parent to who you are paying support and there are no limitations on how that money may be used as the underlying purpose of the child support is to increase the custodial parent's household income. This concept is true in most all states.
That said, Nebraska has this law that may help. It states:
4) In determining the amount of child support to be paid by a parent, the court shall consider the earning capacity of each parent and the guidelines provided by the Supreme Court pursuant to section 42-364.16 for the establishment of child support obligations.
Upon application, hearing, and presentation of evidence of an abusive disregard of the use of child support money or cash medical support paid by one party to the other, the court may require the party receiving such payment to file a verified report with the court, as often as the court requires, stating the manner in which child support money or cash medical support is used. Child support money or cash medical support paid to the party having physical custody of the minor child shall be the property of such party except as provided in section 43-512.07.
So, this abusive disregard standard has to be met.
You final option is for you to then seek to modify custody so that you now become the custodial parent. If you want to do that, you must show that a material change has occurred and that now it is in the best interest of the child for you to have custody.
The case of Davidson v. Davidson, 254 Neb. 357, 576 N.W.2d 779 (1998), indicates that in determining a child's best interests, courts may consider factors such as general considerations of moral fitness of the child's parents, including the parents' sexual conduct; respective environments offered by each parent; the emotional relationship between child and parents; the age, sex, and health of the child and parents; the effect on the child as the result of continuing or disrupting an existing relationship; the attitude and stability of each parent's character; parental capacity to provide physical care and satisfy educational needs of the child; the child's preferential desire regarding custody if the child is of sufficient age of comprehension regardless of chronological age, and when such child's preference for custody is based on sound reasons; and the general health, welfare, and social behavior of the child.