I really like what you have done, and I miss not having rabbits outside. Here are some of the problems I encountered.
I used to have rabbits outside with a similar set up. I put their cages inside of their hutches so they could go in and out, and I would lock them up in there at night for safety. I had to put wire inside the pen (hardware cloth) on the ground all around the fence to keep them from digging out. I ended up using the coated wire because one of my rabbits cut his paw on the wire trying to dig out. Rabbit tunnels can go long distances, so I would only let them dig so far, then I would fill it in and set something over the hole so they could not dig in that spot again. The pen was close to a tree, and my rabbits got tiny ticks that were brought in by birds. If mice got into their hay, the rabbits would get tape worms. I got some Revolution from the vet, which solved the parasite problem. I do feel that my rabbits enjoyed being outside more than they do inside. I enjoyed having them outside because that is where I like to be in the summer. My dream was to have an outdoor chain link covered pen, but I ended up bringing them inside. We also had a problem with a person in our house having allergies, and outside was where they needed to be. Because of the cost of the Revolution, keeping them outside was expensive, but it allowed me to spend more time with them, so I feel it was worth it.
I now have them inside the house. Coyotes and red fox have moved into our area. I have watched a fox jump over a 4' chain link fence with no problem. I think it possible that a coyotes could do the same. They were not in our area at the time I had my rabbits outside. We also have eagles and hawks in our area. I provided plenty of cover for my rabbits, but one day I saw hawks circling above.
I would like to make it safer but I live at home, so feel bad of changing. When I’m planning after being done with my studies and move to an apartment. I have foxes in my area and also hawks, eagles and my neighbors dogs. But, also a cat that will patrol the yard and spend a few hours with the bunnies.
Most people that own dogs in my area, let their dog run lose without leash because I live next to a forest (2 min walk from my house).
But my dad it’s always home and their cage it’s near our bedrooms. So we can hear them if they get scared. We also installed a lamp that will get turned on if something of the size of a cat move onto the yard during the night.
Myself have seen rats and mouses but never near the rabbits cage. So there are a lot of things to think about.
The net on cage will only keep birds away because they can see it from a distance. Creating a safe space for them, but if it was a permanent cage, I would build a real run instead.
One of my bunnies can’t be indoors, she became really stressed and aggressive. She literally messed the whole house during nights. She only became calm outdoors.
The other bunny was really scared of humans, being outdoors helped him to slowly get used with humans and learn to trust people. He will soon become an indoor bunny.
I always fill their hole up when it become too deep or dig the wrong way. They can never disappear under the ground.
I remember couple of years ago with my first bunny, my dad ran out with a broomstick in the middle of the night with only his underwear to chase away a fox from the yard. Because my bunny started to thumping in the cage, waking everyone up. That was the last time the fox came to the house, that bunny only lived to 8 years (passed away because of GI stasis).
Myself also have to vaccinate all my bunnies and watch everyday after ticks. At least I don’t have to worry about snakes because they’re only exist one venomous snake and there only exist 3 species of snakes.
So it’s not completely safe having my bunny outdoors, I can only make it as safe as I can. Most people often use dog run to build the pen for the bunnies. My neighbor have done that with mesh on top, it become a lot safer. They will often have soiled ground or mesh on bottom of the run.