Do you have a capable engineering mentor on your team or in your area that can sit with you and review your work? You'll get a lot more from that than you will from this forum, unfortunately.
There are a lot of problems here -- and that's okay. We all learn by trying new things and making mistakes. In drive design, the devil is in the details a lot of the time and your modeling isn't very detailed, so forgive me if I've made incorrect assumptions in the advice I offer.
1 -- It looks like you're using Pro/E. You have my sympathy.
2 -- Do not use C-channel to build your frame or otherwise expect to add a VERY rigid (i.e. thick) piece of wood or aluminum plate to the inside to add rigidity. You'll otherwise have a lot of flex in the frame -- I know this from experience. The problems you're anticipating with using rectangular or square tubing aren't real.
3 -- The Toughbox Mini with long output shaft driving the center wheel is supported in two places in the Toughbox housing. That puts the load on that shaft at 1" (channel leg height) + spacer + sprocket + 1/2 wheel width away from the bearing. That's probably 2.5" -- too far. There's all sorts of detail missing with respect to how you're going to position the wheel on the shaft -- is it retaining clips? spacers? Retaining clips weaken the shaft. Spacers will exert an axial load from the wheel onto whatever surface (presumably the channel) the spacer works off of. How will you handle that thrust loading?
4 -- You've said the C-channel is 2x1 -- presumably by 1/8" thick. That means the blue parts you show as your dead-axle support are 2.25 x 1.125 x .125". That size isn't commercially available to my knowledge. How will you manufacture those parts?
5 -- It doesn't matter because they won't work. You've got a hole in blue channel and a slot in the frame channel along side slots for mounting the blue channel. I presume those mounting slots are for chain tensioning. Think about what happens when you slide the blue channel away from the center when the chain is under tension. Your axles will not remain parallel to the center axle/toughbox output and you will throw chain and add a lot of drag to the drive.
6 -- Is each Toughbox attached with only two screws? That's going to exacerbate the flex in your frame. Follow the loading -- weight of the robot passes through center wheels, bending toughbox output upward. Flex in output shaft tries to rotate the entire gearbox housing about its mounting point. This is hard to describe, so you have my apologies.
7 -- The location of the sprockets doesn't matter. All of the loading is passing through bearings / hubs in your wheels. The sprockets are floating around the shafts and your biggest concern isn't torque applied by the chain bending your axles in a horizontal plane, but torque applied by the weight of the robot bending them in a vertical plane.
None of us get things right the first time -- or the second, third, or fourth. After looking at a design for a long time, it's hard to be objective about its strengths and weaknesses, so asking for advice from new sets of eyes is a good thing. If some of the things I've written don't make sense, I apologize, but I'm in a bit of a rush this morning -- I've got presentations to give this morning on drive design
