I am trying to find out what the law is concerning my moving out of the State of Iowa and what the laws are involving transportation costs for the children during visitation.

Consult the Iowa child support guidelines.
http://www.judicial.state.ia.us/CSG_charts_and_worksheets/
Modifications of Orders

The court may subsequently modify a child support order if there is a substantial change of circumstances. Iowa Code section 598.21(8-11) In determining whether a substantial change of circumstances has occurred, the court shall consider among other things:

Changes in the employment, earning capacity, income or resources of a party.
Receipt of an inheritance, pension or other gift.
Changes in the medical expenses of a party.
Changes in the number or needs of dependents of a party.
Changes in the physical, mental, or emotional health of a party.
Changes in the residence of a party.
Remarriage of a party.
Possible support of the party by another person.
Changes in the physical, mental, or educational needs of a child.
Contempt by a party of existing orders.


You may need to go back to court and seek modification if you and the other parent cannot come to an agreement.