I think that the expectation should be that there has to be word from a parent--not from a middle-school friend--if there is to be a change from the usual procedure. Therefore, I agree with the advice given by leejosepho.

I would not take offense at the other parent. These things happen. Just let this incident go other than to clarify what the other parent wants you to do if this happens again, and decide whether you are willing to do that. I do not think that you should be expected to stay in a parking lot indefinitely if the other parent cannot be reached.