You definitely have to hang the second bag down low with a bag strap.

Unfortunately I don't have one and have had some nasty tangles trying to rescue a heavy messenger bag as it began it's slide off the pole. Once I got my arm caught in the strap somehow and with the bag twisting and falling I wound up pinned to the suitcase. Pain and a giant bruise.

The good news is that if you can get the bag lower down resting on the front of the suitcase it takes the weight off of the arm you are pulling the roller bag with. Makes a big difference. Also it prevents excess strain to the collapsible handle.

I've been looking for another suitcase which is the only way I know to get rid of the problem.