To be honest, your coop is larger by a darned sight than the coop our next door neighbors have for their 3 chickens. As their flock got larger, they added a second coop, but still a pretty small one. But their white chickens decided they'd rather fly up into the trees at night. When we decided to get ourselves some chickens, we decided to go with a pre-fab coop. My husband is handy, but if I'd had to wait for him to put something together, we'd be lucky to have chickens by the end of the year!
Our coop is very similar to the second pre-fab you have pictured, though it's up on "stilts" Ah, here it is:
Allegedly, it's for 6 to 8 chickens (yeah, right), but it works perfectly well for our two. And I'm still hoping to attract the neighborhood "free range" chicken to join our flock. (Long story - another time.)
I take it you're in the UK. We're in France, and I'm finding that our predator situation is considerably different from what many of the US folk are facing. Plus, the attitudes toward keeping chickens (or any sort of animal) are different.
We started out by putting the new chickens in the coop at night (right around sundown) and letting them out first thing in the morning. By their 4th or 5th day here, they went into the coop when I showed up ("to tuck them in") and now it's just a matter of herding them toward the door as it's starting to get dark. The neighbor next door found that his flock just head for the coop on their own, so they don't bother opening and closing the door anymore. It may just be a matter of putting them in the coop at night for a few consecutive days. I think you've built a lovely coop - just give them a chance to get used to it.