You can indeed re-enter Canada using a private vehicle but your NEXUS Card may not help. Your NEXUS Card is for easing travel between both countries – it doesn’t verify your status as a permanent resident of Canada. Though they may let you in with it, they may also want proof of your permanent resident status in Canada. (This depends whether or not you are asked these questions.) We strongly suggest having a copy of your Confirmation of Permanent Residence (or Record of Landing or Verification Status) with you as well.