I have dragged a component "my-cart" in a parsys which was embed in another component "login", but when I want to edit the cq:design_dialog of "my-cart" in touch ui, I got this issue in console(see the context below), and then all of dialog cannot open.
In my experience, design dialogs and touch UI don't go very well.
The only way to get a design dialog to open in Touch UI is if you embed it into the page component via data-sly-resource with the path as a parameter. Dragging and dropping into the par will not work in Touch UI, but will work in Classic UI. Try and see if this works for you. This works for me in 6.2, so not sure if there is an issue, it may be a 6.1 specific issue.