The S10 has an ABS brake anti -lock system? If so, it is possible that when you step on the strong brake, the ABS module detects the lock or blocking of a wheel and establishes the limitation of braking to that wheel (so it seems that the brakes skate) you will also notice because the brake pedal is hard and because the brakes vibrate, and sound like a snoring, as if they were in poor condition.
If the ABS brake anti -brake system detected some failure, both in individual speed of the wheels and in pressures or in drive valves or compensation pump, be sure that the ABS fault witness will turn on immediately, if this passes, the vehicle will stay with conventional brakes, that is, if you pass it by braking the wheels and skid.
If you did not have ABS system (I doubt it) it would be necessary to think about some obstructed hose or the braking compensator depending on the charge in poor condition.
All the best.