Is this problem specific to mobile devices, i.e. it works in a desktop browser?
It's difficult to answer your question without looking at your site, but I think this may be due to the window mode that you are using. By default Wade uses windowMode == 'full' which means it will try to use the whole window and catch all mouse events on the window. It is possible, however, to change this default behavior using the container window mode. This can be done in the editor from the scene properties tab (remember to do it for each one of your scenes), or in code, after a scene has been loaded, with wade.setWindowMode('container').
However I would not recommend that, because then you won't get the automatic resizing of the game area that you get with the 'full' window mode. I think it'd be easier to put your games inside an iframe without changing any code.
I hope this helps, but if it doesn't and you want to share a link to your website I can have a look there.