2000 Dodge Neon Rear tire locks up after rain

Hello. I have a 2002 Dodge Neon SXT. The problem that I am having has occured about 3 times in the past year and always happens like this:
I reverse out of my parking space and put the car in drive. I drive (slowly) for a few seconds and all of a sudden the wheels seem to lock up. The car feels like it is being dragged and leaves skid marks on both sides. If I stop and try to drive, it continues to drag, but then leaves skid marks only on the left side. It feels like the left back wheel. I have to put the car in reverse and then it will drive normal. The brake light on the dash does not go on, and I never use my parking brake. Brakes have been checked, I've had new tires put on since the first time this has happened. I don't know if relevant, but when this happens & I put the car from park to reverse, the car "jumps". If you have any advice or ideas I would so much appreciate it. THANK YOU! :)

It has power disc brakes on the front and drum on the back.

Thanks!

Wendy