I used to haul out almost every day, to use an arena, then spent more years hauling once or twice a week for lessons.
I also keep a duplicate set of items in my trailer dressing room. What I do differently than what you have described is that I wouldn’t haul my own water to a place where I had a membership located just 30 minutes away, only empty buckets. Is it not possible for members to fill a bucket at this facility? I do like to keep one or two of those blue water totes in my dressing room, just in case, but I rarely would need to use the water.
I also would not clean out the trailer at the other place. In a half hour ride, my horse(s) would poop the obligatory immediate pile right after loading, then probably not again on the way there, but once more on the way home. A couple piles would be quick to deal with at home (although I do have an extra fork in the dressing room). Horses kicking out manure as they are unloaded has never been an issue for me.
If heavy, thorough grooming would be needed, I would most likely do that the previous day, and just do touch-up at the new location. I’ve always saddled at the place to which I’ve hauled. I tote my tack in a small cart to and from my trailer, rather than make multiple trips – my cooperative horses would willingly walk along with me if I did this, assuming I needed to do so, but I would rarely be that short on time.
I also try to have the hay already bagged, either the night before or I fix an extra bag while organizing their breakfast hay; actually, I prefer to get the entire day’s hay together at one time, anyway - so that I only get hay all over me once - therefore it’s no big deal to fill an additional bag, which only needs to be a small one considering the brief trip. I have also found, when making a very short trip (and thirty minutes may qualify), they eat so little hay during that time, that I might not even bother with a bag in the trailer. If they’ve been eating all morning, so have something in their tummies, then the few mouthfuls eaten in the trailer won’t make much difference, IMO. To be clear, I wouldn’t haul a hungry horse without a hay bag.
Where I use time is in cooling a hot horse out before loading for the ride home – I’d rather spend the time saved elsewhere on that.