1997 Toyota Avalon braking problem

Hi- I just bought a used 1997 toyota avalon from my trusted mechanic- alot of work was done to ensure safety for my daughter- i have been driving the car for the past 2 days since i got it home and notice a bumping everytime i brake- the bumping is definitely in the brake area and is not an ABS bumping sound( I am very familiar with ABS brakes and sounds) I feel like there is no control in the brake area and do not feel comfortable with my daughter driving the car- We put new tires on the car- my mechanic says there is plenty of meat on the pads- also, when i run over a pothole, the car feels like it is all over the place- Again, i feel little control when that happens- Any suggestions for me to tell my mechanic?
Thanks
Lauren