I had a similar situation with a dc family that I ended up terming bc this was the straw that broke the camel's back. It was 20 mins past the kids' pickup time, so I called dcm -- no answer. Left a message, waited 10 minutes, then called again. Same thing. So I called the emergency contact (single mom, so no husband to contact first) -- no answer. My daughter was due at 6 for a dance rehearsal, and it was now 5:30. Finally, at about 5:45, the mom called me back and said she was having car trouble. I asked where her emergency contact was, and she said that person was with her, helping her with her car!
So instead of calling me to let me know she would be late, and sending the emergency contact to pick up the kids, she had the emergency contact come and help HER instead. She ended up picking the kids up 2 HOURS late, at about 7:00. I was fuming. I had her term papers ready at the door, and after that I wrote into my contract that I MUST be able to reach either you or your emergency contact at all times, and I must get a call back within 30 minutes or they will be termed. All kinds of scary situations were running through my head, that's a serious safety issue if you have an emergency and can't get in touch with anyone to come pick the kids up. I would NOT let this one go.