The sense seems to be that Maureen Lipman played an excruciating grandmother -- Maureen Lipman's (rendition of an) excruciating grandmother.
Melvin is her fictional middle aged son.
"some children talk to their parents" implies that Melvin doesn't phone his mother (the excruciating grandmother).
Yes, the underlying message is that you should call your parents more often, especially if you're paying BT for the call.
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