Landlord rights when inspecting property

My husband and I are in the middle of a years-long dispute with DMI property management regarding roaches in our building. They have insisted that our apartment is dirty, which is contributing to the roach problem - we maintain that our apartment is perfectly clean (it is) and in fact alone of the apartments on our floor, we do not have a roach infection at this time, as we simply hired our own exterminators and took certain steps the last time we were infested, which was about two years ago.

Yesterday we received a notice through our door that they have received information that our apartment is not being maintained at the contractually obligated standard. This is untrue. Our floors and surfaces are clean, our litter scooped, our carpets vacuumed and our tiled areas swept. At most, we could stand to give the kitchen floor and bathtub a scrub. They now want to schedule an inspection to check our apartment for cleanliness.

I strongly suspect that our landlords would very much like it if we left the building. We got our apartment before the rent explosion and if we were to leave they could re-rent our apartment for more than $1k/month more. In the past, we have struggled to get them to take the maintenance of the property seriously. Our apartment is clean but cluttered, and I think this is an attempt at harassment.

During an inspection like this, what is the landlord legally entitled to inspect and what is the landlord not entitled to inspect? Where can they look, at what, and what kind of complaints are they allowed to make? Am I allowed to record video of them conducting their inspection? What other steps can/should I take prior to and during the inspection to protect myself from false allegations?

Thanks very much for your help.