Can we put in our agreement that one spouse shall have custody and legal decision making rights?

Yes, you may put this in the agreement and the court would probably not object to it. You may also opt to put in a requirement that the spouse consult with the other spouse on specific decisions, like education, religion, etc.

This type of custody arrangement is referred to as sole physical and legal custody. It is the most common arrangement, but joint legal custody or shared custody has become quite popular over the past decade. Joint legal custody is an arrangement where both parents are legally involved in making all decisions pertaining to education, health, and religious issues just to name a few.