I'm looking for some luggage that could start out as of carry-on size plus "personal item" (like a duffel) for our flight (checking the carry-on is not a problem) and then somehow combine into a single piece of luggage (such as strapped together) because our tour's luggage service is restricting us to a single bag each (at 20 kg). We cannot manage a medium size suitcase that weighs 20kg, because of our backs and because of the size of our car. We need to travel with two lighter and smaller bags.
There are luggage sets that combine a bigger bag and a backpack, such as Eagle Creeks Switchback series (http://shop.eaglecreek.com/switchback-carryon/d/1283_cl_-1). You could pack bulky lightweight items in the big part and heavier small items in the zip off daypack. Split them apart when driving, then zip together for the flight and tour. (other companies may offer lower cost versions of the concept).
Or as Nate mentioned, use two smaller soft-sided bags and a bigger basic duffel to carry them both on the flight and tour. I often pack two smaller bags into a larger duffel when traveling and restricted on how much I can check in.
I find the Patagonia Transport Tote 20L perfect for the purpose you describe. It has a 'sleeve' on one side, allowing the tote to slip over wheeled luggage handle. I don't know where you're located, but here's the link to the US web site: www.patagonia.com/us/product/transport-tote-20-liters?p=49460-1
This is quite common for backpacks. The one I use is from Monterra which is available in multiple sizes. It splits into a small daypack and large backpack. The nice thing is that it does not have to be used as a backpack. The straps fold inside a zipper compartment and there is an add-on shoulder strap, so that it can be used as a large shoulder bag. When need to have a single piece, both halves attach together with a zipper plus 4 clips for added security.