Does the mission change when the passengers change?

I really don’t think this will translate well to the blog, but here goes anyway…
I was dropping Paco off at his friend, Josh Daniels’ house. (names are changed to protect innocent).
Nadia was with me. We had walked over.
When I arrived there, I saw that another family, the Smiths were there for lunch.
The Smiths know where I live and said, “Oh, are you headed back to your house?”
I told them I was.
“Our daughter, Gina (age 8), is going to her friend, Amy King, who lives down the street from you.”
I responded, “I’m happy to take her there now,” seeing as Gina would be able to get to Amy’s house anywhere from 1 to 2 hours earlier than if she waited for her family to finish lunch.
At first, Gina (who has knows me—she’s in the same grade as Paco), indicated she would rather stay with her family, but while I was organizing the return plans for Paco, Gina changed her mind.
No skin off my back, I was headed in the direction of the King’s anyway.
So, Gina, Nadia, and I left the Daniels’ house and headed for my street.
Where things get interesting….
Along the way, I saw my friend, Jon Cole, walk out his front door and, since we were at the halfway point, I turned to the girls and said “do either of you need a bathroom stop?”
I had been walking with Nadia for about 45 minutes and if there’s one thing in which I believe in, it’s pre-emptive bathroom visits.
Both of the girls said no.
Jon said, “hey, you want to come in for a few minutes just to chat?”
I said, “well, are you guys having dessert? Maybe I can hook up the girls with a cookie?”
He said, “yes, we’re having dessert.”
Turning to the girls, I offered them a cookie. Nadia said she was interested. Gina said she wasn’t.
Now, you should know that Gina had never met the Cole’s before, but my assessment of her character was that she is pretty happy, go-lucky (we had been chatting along the way) and that a short detour wouldn’t be a big deal.
We went in, the girls sat on the couch and we were there for a maximum of 10 minutes. We took our leave and I safely delivered Gina to Amy’s house.
The Questions and The Controversy
Here’s where you get to vote/decide/weigh-in.
The NFO thinks that once I accept the responsibility for delivering Gina to Amy’s, I have no right to detour from that mission.
I think that since I am doing Gina and the Smiths a favor (one I am happy to do), that I am able to keep some degree of flexibility in how I get her there.  I would agree that a visit to the Cole’s of 2 hours would be excessive, so there is some point (for me, it was more than 10 minutes), at which point it is simply not right to stay and not fair to Gina. In my view, Gina comes out WAY ahead in terms of when she gets to Amy’s house, regardless of whether I stop at the Cole’s or not.
The NFO, however, disagrees and thinks that the point is 0 minutes. Once I take the job, I lose all flexibility.
Analogous might be….you offer to give your friend’s child a ride to your next door neighbor’s house from soccer practice. On the way, you pass the drugstore and you remember that you forgot to pick up a birthday card for your Mom. You see an opportunity to get it.
Is it ok to park, run in with the 2 kids, get the card, and run out? (assuming it is 10 minutes or less AND there’s no explicit time expectation for when your friend’s child will arrive at your neighbors)
Anyway, as I said, it doesn’t translate perfectly, so fire away.