It’s as good a plan as any and better than some I’ve seen. I like the flexibility the two runs give you to deal with problems you can’t even envision you might have.
I don’t know how many chickens total you are planning on having or the type of sod and soil you’ll have. I have an idea of your climate which is not too bad for getting grass to grow. There is a real possibility your chickens will wipe out all vegetation in both runs if you let them. They don’t just eat the grass; they scratch out the roots and eat those too. It’s possible you can keep some grass but not very likely unless you sacrifice one run and let the other recover.
I don’t know where that smaller brooder/coop is but if it is attached to one of those runs so the chicks or chickens in it can have access, that is even better.
One thing I suggest you consider. If the runs are on opposite sides of the coop, the chickens can’t see each other if you are raising younger chicks in the future. It could help integration if the runs were set up where you could keep then side by side where they can see each other and get used to each other. I don’t know what your management plans are about adding replacement chickens in the future.
Several people use the mobile coop idea, usually with a chicken tractor but there are other methods too. Some challenges with them are that if they are very big, they can be hard to move. If you have nests they can get a bit heavy unless you are careful how you do the nests. The smaller they are, the more often you have to move them or they totally wipe out the grass and the poop can build up and get stinky. It’s sort of a catch-22 but many people manage, especially in the good weather months. There are a lot of clever, hard-working, ingenious people on this forum. Using PVC instead of wood to keep the weight down comes to mind.
Some other things. It can be challenging to make those mobile runs truly predator proof, especially if your ground is not real level. People do it, it just can be challenging. Another possible concern. How do you get the chickens to and from the coop? Hand carry them morning and night?
I tried a chicken tractor one summer and decided it was not for me. But others so it and are real pleased with them.