I've read that some places use a much too strong mixture of soap, or too harsh of a soap in order to get more dirt off the car (get rid of the film that's usually left behind, that you'd have all over your drying towel if you were to wipe the car without washing with a mitt). As most of the coin ops here are totally self serve, and the ones that do have "attendants" don't have any knowledge of the products, other than"fill this jug with the white stuff, this jug with red stuff" you probably won't be able to find out what brands they use. If the soap is harsh, then you will likely be disolving the wax pretty quickly. Sealants, I don't know.
What I've been doing lately is going to one of the "pay by the minute" places. They don't care if you bring your own bucket- they probably prefer it, as it doesn't cost them anything extra. You can use your own stuff and use only their water and heat. If you felt the urge, you could even wax it there, thus helping 'up' winter protection! One word of caution, though, is that, unless it's a "bad" day for washing, you'll likely be in there with lots of others, as there are usually 6+ bays, partitioned off by only a tarp or small wall on either side. This leaves you exposed to all the steam, water and mist from neighbors, so you probably would want to go early in the morn to avoid this. Also, if you plan on waxing, bring a wax that doesn't need to haze dry, as these places are often humid all the time, so why pay extra time waiting for it to haze and run the risk of overspray attacking the wax? I've been able to do "quickies" in about an hour, which here costs about $10.00-Pretty cheap, I think, since I'm getting a thorough wash and quick wax, versus a spray only and it would still cost around $4-$5.00, with poor results-streaks, film, etc.
My fingers hurt
Just my thoughts.