I can't understand why your DH has flown off the rails. You have every right to say to nanny that you don't want your DS spending time at her house. But, the fact that she has assumed it is okay is not really cause for alarm. It is just cause for a casual chat and clarification of what you do/don't want.
Tell your DH to settle down. I can't really see this is worth freaking out over. Just talk to the nanny and tell her what your expectations are.
It is possible she just popped in for 5 mintues as they passed by and so didn't think it a report worth event.
If you asked me what I did yesterday, I would probably say I went to work, spent too much time on MN, and went home and saw the kids, put them to bed and cooked dinner. AS it happens I also stopped at Tesco on the way to work, but I would probably not mention that, and not because I was intending to deceive you.
If you don't have one already, I would highly recommend a nanny diary where you can read in more detail what they have done with the day. Just get one and nanny, babysitter, and you can all write in it. And, it makes a great keepsake in later years.