Problem stated by OP: Camera is using slower shutter not higher ISO
Real problem: OP is letting the camera do the thinking instead of the person holding it
Solution part 1: get it the hell out of P mode

If you want to control DoF, don't care about shutter speed as long as it's above a certain minimum, and prefer the ISO ramp up instead, set Av mode, ISO to Auto, and in the menu where you set ISO range, set the min shutter speed you want.