I know for cats they have doors that only open if they have the right collar on, so maybe they could get one like that for the dog? I think it's some electronic signal or something that opens it if the signal is present or in the absence of the signal it won't open. I believe they make these for cat doors because other critters (such as raccoons) have been known to come and go through non-monitored doors. I think this would be the perfect solution, and I don't think they are all that expensive.

Good luck!