Query Multiple Taxominies Across Multiple Post type’s

At a glance, I would guess that the problem is your use of

'relation' => 'AND'

Using AND means that you will only return items that fall into all of the taxonomy terms. If you want to return items have any of the taxonomy items, change it to

'relation' => 'OR'

If that “doesn’t work”, please provide more details about what “it doesn’t work” means 🙂