The coop structure you want rodent-proofed is the one with the security door, correct?
In my area, rodent presence usually means there will be rattlesnakes coming by. Old coop had a lot of rats and mice that would come by at night; I've got young kids who play in the yard and a wife who's biggest fear is snakes. Because of that I decided to build a new coop and thought a lot about how I was going to tackle this specific issue. Have seen no evidence of rodents at chicken area since building new coop.
From the bottom, the wood section has large holes - like in the corner where the rope hangs. A simple vertical L-shaped corner piece screwed over the top could easily resolve that issue. Aesthetically it will look much better too
Next up, if the wood is secure the rat would climb up to the fence to get inside - ideally you'd want to replace the chicken wire with 1/2" or 1/4" hardware cloth, which has small openings and is a welded wire/stronger. I suppose if you already had a roll of chicken wire on-hand and don't want to buy anything, you could potentially add multiple layers so the wire is offset to try and simulate smaller openings and add to the wire strength. If I was relying on that method, I'd probably "weave/sew" the fence layers together with galvanized wire (or hog rings) so they don't separate easily.
Lastly, if the rodent climbed all the way past to the roof section, they'd just go up and over the top or under the roof corrugations. Once they figure it out, that'll likely be their regular route. On my roof I used corrugated panels on 1x4 purlins. I cut hardware cloth to fit tight against the corrugations and installed in on the inside.
Hope this helps