The easiest way to deal with this is to get rid of the rotational motion altogether. Without the moon being in orbit and the Earth rotating, the tides would still be there (for a little while, anyway - until the moon crashed into the earth!).
Exactly! The only thing necessary condition for tides (or differential acceleration) is that the object be in free fall. The effect of rotation enables us to "see" the tides by standing in one place, and the effect of orbital free fall keeps the whole experience going on and on.