We had had our car repaired by the mechanic whose telephone number you had given us, we continued our journey.(In your opinions, it is incorrect)
If we insert 'and' before 'we continued', 'we had had' is acceptable, but 'we had' is sufficient.
reduced
b- Having had our car repaired by the mechanic whose telephone number you had given us, we continued our journey.:tick:
and we can use a present participle instead of a perfect participle to indicate the first act if it and the second one happened successively.
- Having had enough, he left the table.= Having enough, he left the table.
I think that 'having had' is better unless the finishing and leaving are simultaneous. Even then, I prefer 'having had'.
but if the first happened for a long time before the second , a/the perfect participle must be used
- Having failed twice, he didn't want to try again.:tick:
So I think it should be
c- We had our car repaired by the mechanic whose telephone number you had given us, and we continued our journey. Fine
reduced
d- Having our car repaired by the mechanic whose telephone number you had given us, we continued our journey.
because "We had our car repaired " and "we continued our journey" happened successively. - and so 'having had is better.