Not saying anything pro or con about her because the whole thing is nonsensical to me. But...
when I travel and someone from my home is picking me up at the airport, I don't carry my keys. Just because I don't want to lose them through TSA or anywhere else.
I think that the first thing she would have noticed upon arriving at the complex is that the Nissan was not there. So, why be nervous to enter the apartment as it appeared he and the kids were not at home?
A wellness check is not a full battle dress with police knocking down the door. The apartment super would go and a walk around would happen. The police might enter if they have permission from the renter to see if anything is wrong. Yesterday, the grandmother said she talked to a cop in the parking lot for help. Curious and curiouser!