Why do the ABS and Brake lights stay on?

The ABS and Brake lights stay on when the Abs computer has detected a malfunction and set a trouble code. You need to have the system checked for codes.

were could some one take theirs to to have it checked?

You should be able to check the codes yourself. Get in the Durango, shut the doors and put key into the ignition. Turn the key as if you are starting the truck but stop at the accessories or power on position. ( the position right before it turns over) you need to do this quickly 3 times back and forth and end in the power on position. Your computer on the dash will flash all codes that it has detected. Then go to

OBD-codes.com and look them up.

Good Luck