It’s the post-ride transfer that is the issue. Little one is a DEMON for waking up and staying awake when you don’t want her to! Otherwise I’d be out razzing already!
Fair comment; my daughter was the same TBH. Never ever managed to move her when she was asleep.
My niece was the opposite; could be moved from house to car to bed with no issue. I'm not bitter at all...
Take them in the cargo bike. I'm sure the rocking will send them to sleep!