This varies from council to council (just like everything else about GS, it seems

) Our council's day camp is run by paid council staff. If leaders volunteer as aides, you get a discount for your daughter to attend the camp.
A week at day camp Monday to Friday costs $275. If you are in the horseback riding program it costs $375 for the week.
We get a deep discount (pay about 1/4 the fee) as volunteers. Is the day camp you are referring to at a GS owned/ran camp? Most of those do have paid employees. ETA: just reread the part about horseback riding, so my guess is that it is at an actual girl scout camp.
Our day camp is ran by the SU and is held at a private wilderness club/campground. No one from council works at the camp (while I guess they could volunteer, but it wouldn't be a paid position through the council). Speaking of it being a private camp, part of the agreement is that we have access (but not private access) for 2 days of training and open house. Most of us are there all day during the day that Sunday for setup, but the members are allowed on the property while we are setting up. Open house is several weeks before actual camp. The parents get a tour and orientation while the girls get to know their unit leaders and the girls in their unit.
Since my earache is keeping me up and the noise from the TV hurts, I've got nothing else to do but say a little more here LOL.....
I'm trying to recall the setup in the bathrooms at all the resident camps I have been at. Right now I can only recall 2 clearly.
One is the lodge that the troop rented for troop camping. The other is 2 different platform tent units at another camp. DD has attended resident camp there, and the troop has camped there in the fall.
In both situations there were a few shower stalls, with a bench and hooks across from the stalls. The girls would be able to shower privately, but the changing area is open to everyone in the shower area. I wish I had the resident camp literature from the parent packet, but what wasn't signed and turned in was thrown away a long time ago. I know they addressed modesty a bit and suggested that girls with "issues" shower in their bathing suits. They even said to save time, all girls would be asked to buddy up to shower in their suits. this was not mandatory. The girls did not have to buddy shower.
I do know that at the lodge troop camping the girls were sent into the bathroom to change in small groups. For some reason DD and the girl she was buddies with ran back into the main area in their underwear. One of the leaders pulled the girls aside and explained to them that they weren't suppose to run out in front of the leaders unless they were fully clothed.
I'm sorry if my opinion comes off as harsh. If I was in the OPs situation, I might be the one calling around too. However having worked with day camp for 2 summers and with the troop for 4 yrs, I am coming from a different prospective. Sure the first yr I volunteer for day camp I rolled my eyes at some of the rules, especially the no running anywhere other than the open field. However I quickly changed my mind the first time I saw a girl go face first down the gravel road that leads down to the office and lake. I don't make the rules, and while some of them I might not agree with at first, I can't think of a single rule that I disagree with after spending a week at day camp.
As I have said before our day camp is a bit unique because it is not held at a girl scout camp. We rent it for the one week a yr. For that week, members of the club are not allowed on the property from 8:30am until 3:30 (or maybe 4)PM. Twice this summer I was present when members came onto the property. One was the last AM. I had picked up a friend that AM and as we parked we noticed 2 women unloading several large dogs from 2 vans. My friend walked over and asked the women to leave. They refused and we had to get one of the camp directors up to the parking lot. the women had taken off on the walking trails by the time the director arrived. My friend and I both had to report to carpool duty so I don't know what happened. The other incident was when several men and kids came running onto the boat dock while my unit was canoing. I asked them to leave and they started in that they were members and had every right to be there. Just as I was about to explain, one of the male volunteers came up and asked them to leave. The didn't question him. Luckily it was about time for us to start carpool so the male volunteer was getting the boat ready for carpool.
The yr before the camp treasurer who also teaches canoing was threatened by some guys that came to kayak.