Muffet and Jillp, you are both failing to take tense into account. In the simple past, 'but' cannot follow 'had to'. For example, "I had to hand in my passport when the Customs Officer demanded it" means you had no option and you, in fact, did hand it in on that past occasion.
But that does not mean one cannot say "I had to be at the station by 10 o'clock but my taxi was late and I missed the train." ('Had to' here implies...if I was to catch the appropriate train.) Your own Examples 2 and 3, Muffet, illustrate the point I was making perfectly. In other words, they refer to "future-in-the-past", as it were. In other words, ideally such and such would have to happen but only if certain conditions were met.
There is not a shadow of doubt but that 'had to' can - perfectly legitimately - be followed by 'but' in certain circumstances, just as I outlined earlier. End of story.