If the weather is unusually hot for the area, a properly sized system may run nonstop >24 hours at a time. After leaving the house during a heat wave with the AC off, it may take several days to recover. Just let it run.
I'd recommend setting the thermostat back instead of turning the AC off when you go on summer vacation. Otherwise the heat and humidity can really build up inside.
The dehumidifier will help with the sweating, and yes, it does add some heat to the space in the process. Once the AC catches up, though, you shouldn't need it anymore.
[Edited by wyounger on 07-20-2005 at 09:32 AM]