Congratulations on finally getting your lifelong chicken dream! I bet your daughter will be thrilled.
It looks to me like your coop already maybe has hardware cloth, and I am totally on board with keeping your girls inside at night. I have limited carpentry skills myself and have to admit to having "temporary" runs on two of my coops -- one of them for several years.
These are by no means sturdy or predator-proof, they're just enough to keep the chickens contained when I let them out of the coops in the morning and before I left them loose for the day. I just take metal fence posts from Menards, pound them into the ground with a cheap mallet, zip-tie wire garden fencing to the posts and attach the netting I use to keep birds off my fruit trees, again with zip ties.
Again, these are certainly far from a "best practices" solution. But it's something just about anyone can do to give their chickens a little more space. BTW, none of my birds is EVER loose or in the runs unless I am home -- even those chickens who have actual sturdy runs stay indoors; I KNOW I have predators here.
Also, you may not be seeing predators, but increasing numbers of wild things are moving into city settings where it's easy to find meals. I had no idea minks live around here -- until one committed a massacre at one of my coops.
Welcome to BYC, Dahn! Let us know how things are going!