katy & i cruised on the radisson
navigator a couple of years ago. we did not bring wine, so i cannot answer that question for you. the wine provided with the meals was actually pretty good & you could "upgrade" from the house selections by choosing from their wine list if so inclined. they allowed me to taste their selections before deciding & i only ordered off the list once.
this is a very fine cruise line. your parents should have a wonderful time & yes, you do wish you were going with them.
in case you haven't looked
here's a link to the radisson cruise line website.