If your preference is a December start date, to the extent you would decline the job if it was only available in September, you don't need to tell them now. You can take a bit of a bet that if you reply to a written offer with another date, they would rather wait 3 months and get you than go through this whole process again to find someone else. If not, well, you had already decided you would decline a September start date.
If your preference is not that strong, then bring this up during the third interview. Say something like:
I know I had mentioned a September start date, but my family has been offered a great opportunity to [whatever your wife will be doing for that break] and I would like to be part of it. Do you think that starting in December is feasible?
On going back and forth you may be able to negotiate something like starting part time in October and switching to fulltime in December. If they won't budge from September, you will have a hard choice to make.
I know it's not fair, by the way, but the reason for the delay matters. If you are going to be a new father, if you wife is going to another country and you'd like to go with her, if you have a chance to be in a reality show, whatever, the actual reason will affect the flexibility the company shows. If it's more like "we are going to sit around our apartment and watch TV and read for a few months" you are less likely to find them amenable to it. So work on your one sentence pitch to explain the delay.