Hocus focus.
Whether you separate the prefix from the verb has nothing to do with it being a question, but rather what you want to focus on. If you have a question word (!) like ki or a phrase like hány nő, they want to be in the focus, of course, since that's what you want to have answered. But in yes-or-no questions like this one, the focus is on the verb, à la "Do you do this or do you not do this?" Thus, the prefix should remain attached.

The preferred translation is "Bemegyünk, ti pedig elmentek?"