I have to say that I think Chuck is right, and that you will not be able to be completely happy about leaving them unsupervised in the largerrun area during the day, even when you are watching from the house. In most areas now, foxes are a menace even in suburban gardens, during the day, especially at the beginning and end, but at any time really. There are people on here who have told heartrending stories of swift and deadly daytime fox attacks, especially as the fox breeding season is now, and they have to hunt even more energetically to feed their cubs. Whilst the hens may be secure in the wire run, this is probably too small for them for longer than a short time, and I expect you have already found that these low, small wire runs are near impossible to clean out daily, compared with a walk-in run which you can enter without bending and crawling. Daily poo picking is essential, not only for health reasons and to prevent smell developing, but to keep the girls' feet clean so that when they start to lay, they dont walk muck all over the eggs. Also, if you can keep the poo level down, there is less risk that the birds will set up a worm cycle by pecking at ground where contaminated droppings lie, and thus re-ingesting worm eggs into their gut.
The best solution in the long term is to instal a secure walk-in run, with foxproof base, 2 metres high so you can walk inside without bending, and with strong mesh sides and roof. Foxes can easily scale a 6ft fence or wall, so the run needs a roof, either of the same wire mesh as the sides, or a solid roof which will also keep out rain and help prevent mud on the floor. Then you can place their coop inside this run, (store the wire run until you need to isolate a chicken one of these days,) and relax in the knowledge that your girls are safe to leave and have plkenty of space even when not out in the garden. There are lots of threads on here about making your owen run, we're always going on about it, so plenty of help is available if you want to discuss ideas and queries.