Because you don’t have a driveway/hose, I would try something like the Simple Green “OxySolve” cleaning concentrate (it says it’s for power washers but there are mixing instructions for “manual cleaning”). Most concrete cleaners have some pretty harsh chemicals in them that could damage your bathtub, but the Simple Green stuff seems pretty tame.
I don’t know anything about the production of that movie, but taking episodes of a canceled TV series and making them into a crappy sequel movie has definitely happened before (see Disney’s Atlantis 2, which was literally just the first three episodes of the scrapped TV series squished together into an incoherent hour and a half montage)