If the park reservations are "sold out," keep checking back, but if you can't get one then yes, your DHS access is limited to park-hopping there. (Anecdotally, even though the terms and conditions say they don't guarantee parkhopper access to parks at full capacity, so far, even on busy days, WDW has allowed parkhopping to parks for which reservations were fully "booked.") Obviously the big loss at DHS is that if you can only hop there after, say, 2pm, you miss out on the chance to join a Rise of the Resistance ("RoTR") boarding group, as that's only allowed at 7am with a park reservation, or 1pm for those inside the park already. Other than that, you're almost better off visiting later in the day anyway, as lines in that park tend to peak in the morning.
As far as hopping back to the park where you started, you can absolutely do that. You can hop around, or back and forth, to as many parks as you want every day, subject to timing restrictions (e.g., 2pm or after, after you've entered the park for which you had a park reservation), or capacity restrictions (which theoretically could limit parkhopping but in practice haven't been an issue in the months since parkhopper returned).
