Well, Till is a veritable fountain of luggage and packing knowledge, but I would modify his suggestions in a few spots. Take 4-5 of incidentals and wash as needed. That would mean a total of 5 UW, boxers, and athletic shorts. One workout shirt. I agree on ditching the shortsleeved shirts. Take 2 long sleeved quick-dry shirts (very easy to find these days) and roll the sleeves if necessary. Your list includes 13 pairs of socks, I know you can cut way down there.
Till is right that the trifold toiletries bags are bulky, but I draw the line at using ziplocks for toiletries. I recently bought an Eagle Creek "Caddy" and am reasonably happy with it. It's smaller than many toiletries bags, has a hook and two end compartments, and holds a surprising amount of stuff.
I've owned many many brands and types of luggage, as have many of those who frequent this forum. By far the best I've ever found are the ebags TLS line. I have the weekender convertible, the 21-inch and 25-inch wheeled duffels, and both sizes of the lunch box "cooler" bags (perfect for LD train and car travel). From looking at the website it seems the TLS Mobile Office as your wheeled bag plus the Weekender Convertible for clothing might work as your combination. Put the laptops in the MO and the iPad in the laptop compartment of the WC.
I would just use two regular old bungees to secure the WC to the MO, very easy to do/undo and stash them in a front pocket when going through security, getting on a shuttle, etc. When you're at your work destination the MO can be wheeled around anywhere, to save your back.
One other possibility is using a small fold-up luggage "cart," with two non-wheeled bags. Back in the days before wheeled bags (some here can actually remember that long ago

), that's what I always used but they were bulky and really heavy then. I think I've seen very small carts at the Samsonite outlet stores. You might want to investigate that idea, but keep in mind the cart would have to be inside your bag at times and the wheels would be filthy so need little caps of some kind to cover them. Try travelite or micro mover for search terms.
One last note, I'm always amazed how much the TLS Weekender Convertible can hold, it's a great bag and I really like the way the backpack straps fit into their own compartment. The fabric and build quality are great on the TLS line. I have the "blue yonder" color and the 25-inch bag has been checked many times with no visible wear and tear - pretty amazing.