The quest "In the name of the law" can't be completed until you have the units on Home Island. This is not made clear in the description. I had all of my Crossbowmen out on an Adventure (Wild Mary) when the Quest appeared and even though I had more than enough in total, it didn't complete the Quest until I'd finished the Adventure and they started the journey home.
The Quest should either include those on Adventures in its totals/completion check or state clearly that it won't.
Obviously some of the Adventures (like Secluded Experiments or the Fairytale ones) have long time allowances and so it could be a week or more before it lets you continue the Event's Quest line because of it. I know you could just hire a hundred more troops in the meantime, but you shouldn't have to.