the question is whether or not the child in question can have the money paid directly to them after they are 18.
Nope.

Also, the mother does not want the child to have the money so, legally, can the child demand the money.
Nope.

Child support is what the non-custodial parent pays the custodial parent as his/her portion of the expenses related to raising a child. This includes not only expenses directly incurred by the child - schooling, medical, food, clothing, and the like - but indirect expenses such as the mortgage/rent, utilities, and so on.

The child is not entitled to a penny of it.