@Ampedup,
you are going over your main breakers amperage load probably adding a portable ac unit is pushing your panel main breaker to the limit if its an older home, new homes have a 200 amp main breaker usually and if its 200 amps you shouldn't have a problem. with the ac unit on while you use the dryer it probably trips, but if the ac unit was off and you use the dryer it probably wont trip.
another thing could be that your portable ac unit is plugged into a regular 15 amp receptacle and may need to be on a 20 amp receptacle with 12 gauge wire, so you would need to read the label on the portable ac and see what amperage it usess