Good question. I have the impression that this was not an act. Columbo really was angry with Margaret. Keep in mind that it was only the second episode and his character was still in development.
They reconciled shortly afterward and Margaret helped Columbo trap the killer. (Just as Joan Hudson came around and helped him trap the killer in "Prescription: Murder")
Correct, that part wasn't staged, because while they shared similar suspicions and discussed the keys in particular at the restaurant, she acted on her own.