my brakes work fine unless i,m trying to stop on ice. they lock up and i hear a noise coming from the passenger side rear it sounds like a louder than normal fuel pump also i hear a slight grinding or rubbing sound only under very low speed braking 10 mph or less also from said side of rear please help i have recently removed brake dust and did a spring job on both sides but problem persists shoes also seem in order however there was a very slight crack in the one shoe on passenger side

Is the cracked shoe on the right rear? If it is, then my bet is the shoe is likely the cause.
FWIW
YMMV