I'm the custodial parent. Can he insist that our child go to school from his home and refuse to take her to school if I register her in my district?

There is a lot here.  Since you are never-married parents, you should look to the paternity statutes to see the presumptive rights and obligations both of you have.  It would also be helpful for both of you to review the Indiana Parenting Time Guidelines.  Hopefully a review of those will center both of you to the best interests of your child rather than arguing between the two of you.   If there is no Court Order, then the only way to obtain enforcable "rules" about your parnting plan is to file a case and request a Judge enter an Order for custody, parenting time, and child support.  The Court will enter an order for these things if you two do not agree, and the Judge's standard is "the child's best interests".  Matters of school and getting to and from there on time with their work done and ready to learn will be a top prioirity.  The IPTGs have a section on transportation. Dad may not be able to hear it from you because he's too angry,  but the reality is that things DO change - kids go to school, get friends, participate in sports - all of those things taking time away from Mom and Dad.  That's life.  Your pareting plan must change with the needs of your child  -  period.  You both will be better off working togehter to figure out how both of you can get as much of the remaining precious time with your child as you can rather than fighting.  If you don't trust each other, file an Agreement with the Court for parenting time to ensure there are enforceable "rules" for the both of you, and understand that this agreement or Order can and should change when your child's needs change.  Good luck.