I am unaware of any law against sleeping in your car, unless of course you are driving. The issue here is where your car is parked at the time you are sleeping. In other words, are you violating any laws such as criminal trespass? Since, from what you've said, you have the owner's permission to park and sleep on his property, criminal trespass is not in play. On the other hand, there may be a city ordinance or other law that forbids sleeping in your car at a shopping strip, though I've heard that Walmart allows this for RVs. Plus, if there are other tenants in the shopping strip, they may have lessee rights that further complicate the matter. My suggestion is that you first contact the local authorities to address your concerns.
DISCLAIMER: This should not be construed as legal advice and is informational only.