Based upon the facts that you set forth in your post, I think the least of your worries is your problem showing the property. Your failure to put the security deposit in an interest-bearing trust account for your tenant is a serious violation of landlord-tenant law. If you sue them, they can countersue you and you'll have to pay all of their attorneys fees and costs plus additional damages, in addition to paying your own attorney to sue them. I would strongly suggest hiring someone other than your son to manage your property. You need to hire an attorney.
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You need to consult an attorney. Failure to properly deposit the security deposit represents a legal problem that the tenants can use against you. On the other hand, if you had a lease agreement, there should be a provision permitting the property to be open for things like a showing. You may have a very tough fight because there seems to have been major issues created by your son's negligence.
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I agree with Mr. Zwaren. You may need to wait for them to leave before showing the apartment as doing otherwise might cause further friction between them and your son.
On a personal note, you sure your son should be managing your property?
I may be guessing or not licensed in your state. No atty/client relationship exists.