In Ohio, can custody of a child be designated in a will?

You'll have to ask a lawyer, because laws vary by state. I'm sure your new spouse can be named custodian of a minor child only if the non-custodial parent agrees. Most of the time, court hearings will be held to determine the placement of minor children if a custodial parent pes; and the judge will have the final say as to the placement of the children. While the custodial parent's wishes will certainly come into play, if the judge doesn't deem the placement in the child's best interests, the judge may award custody to the non-custodial parent.