Why does my brake pedal jerk when I stop quickly?

When I come to a stop sign I press the breakers enough to be able to stop properly but
sor some reason it doesn't slow as fast as I think it should. So, I have to push harder on
the brake. When I do, the pedal jerks up and down. It acts like the t is getting hung up on
something. But when I stop normally I have no problem. I notice it makes re when I am
facing downhill coming to a stop sign. I have very little knowledge of the brake system of
a car. But I do know there is a slight leak in one of the calipers in the back. Other than
that, I just had new break pads put on. One of the pins keep popping off too, s I am
worried that it may have gotten caught somewhere.