the action happened by order and i think that we do not need to use past perfect here.
I agree with you. The sense in which I would use "had had dinner" instead would be to stress that the meal was 'over and out of the way'.
"We were anxious to get going as we had a long way to drive. Mum, as ever, wouldn't let us go without eating, so it wasn't until (after) we had had dinner that we got underway."
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