Yes, it is perfectly correct. Past perfect of "have to" = he had had to And no, it doesn't sound strange to us at all. In spoken English you would here: If I'd had to to.......

'had had' exists as the past perfect form for both 'have' and 'have to' and is therefore also used when 'have' or 'have to' is the verb in the 'if' clause of a third conditional sentence. 'He had had enough to eat, so he declined dessert.' (= past perfect of have) 'Tom was late arriving at work yesterday, because he had had to take his children to school first.' (past perfect of have to) If I had had enough money, I would have bought that dress I saw yesterday.' (3rd conditional with have) In spoken English we normally use a contraction of the first 'had' = 'If I'd had enough money..' 'If I'd had to study for an exam yesterday, I wouldn't have gone to the party the day before yesterday.' (third conditional with have to) You can sometimes replace the past perfect with the past simple if the order of the actions is implied by another word such as before, after, first. 'Tom was late arriving at work yesterday because he had to take his children to school first.' BUT you cannot normally replace it in the third conditional because you then create a mixed conditional. 'If I had enough money ( = second conditional) I would have bought that dress I saw yesterday (third conditional) = I don't have enough money so I didn't buy the dress.

You wouldn't use double had, you would just say "If I had to pass an exam yesterday". Had already implies past tense. You can also say, "If I have had to ..." Just search google for usage examples: http://www.freeadvice.com/law-questions/i-have-had-to-quit-my-job-41789.htm