Why do this in a portal? This looks like it would make much more sense as a list view with fields from the parent table in the header area.
We won't be able to diagnose your issue since you haven't told us what your previous and next buttons actually do? Are they scripts? what scripts?
Previous button is go to previous record and next is go to next record. No scripts. Single action.
Record navigation has nothing to do with portal navigation.
If you want to navigate the portal you need to script using the "Go to Portal Row" script step.