Q: Brakes lock up when wet

My Malibu had been acting up at high speeds, when I would brake the whole car would shake violently and I could feel it most in my foot on the pedal. I had it worked on and besides some residual shaking as the new brakes broke in everything seemed fine. The shaking began again on a rainy morning while I was coming off the interstate, braking..and then it stopped again, I guess because they didn't get wet for a while. Now the last three times they have gotten really wet (we have had some strong storms) Not only will the car vibrate when braking at high speeds but it will begin vibrating just while driving at high speeds. This morning it started and my brakes locked up! What I mean by locked up is the pedal was hard to push...but it didn't matter because I didn't need to push it. The car was in constant braking mode with my foot removed from the pedal and also while hitting the gas. I got the car home, let it dry and later it was fine, it has locked up at lower speeds too when wet

My car has 149000 miles.
My car has an automatic transmission.