Hard braking brakes need to be pressed harder (than my other vehicle) to work

Your better off going by the feel of the pedal rather than measurements. Try this. With the engine off and the brake system cold remove the key from the ignition and pump the brake pedal. it should get progressively harder and your foot travels a shorter and shorter distance until its too hard to press.
Press and hold the brake pedal hard down then start the engine. You should feel the pedal soften, that's the vacuum inside the brake booster kicking in.
Release the pedal and again press it hard down, holding it there. The pedal should feel firm and not change. Release and repeat to make sure.
If the pedal has no resistance check your work as there is no pressure in the system. If the pedal is soft or spongey re-bleed the system starting with the calliper furthest away from the reservoir.

Yes the brakes will always operate properly as in the fact they will stop the car the only issues you will have, is the vehicles brakes will skid if you have to slam them on but normal braking will still operate normal. If the brake booster is bad the pedal will be harder to push but again the car will always stop. The one time you will need to be extra careful would be when raining or slick outside the brakes will skid easier.

Shelly, in most cases, these can be cured by replacing your brake pads/shoes. However, you stated that you are hearing a "pump" sound when you depress the brake peddle. So this is telling me that you may have either a vacuum issue, or having an issue with your "Brake Booster". That also runs off a vacuum. A little info for you. ^^ When your engine is running, the entire system is put under a negative vacuum. This controls things like cruise control, and vacuum assisted brakes. Older vehicle did NOT have a vacuum assist, and were called "Manuel Brake" systems. While these were more reliable, the were harder to push the peddle until the brakes worked. As an example, with your car turned off, depress your brake peddle about 3 times and then try to press it as if you were stopping. You will find that the peddle is much harder to press than if the engine were running under the vacuum. The reason I asked that you depress the peddle 3 times, is when the engine is off, you are no longer building pressure, so this pressure is naturally bled off when you use the brakes. If this does not happen, and your brakes are always hard to depress, then for sure your having a problem with your brake booster. I hope this helps, and good luck. ^^

Assuming you're talking about the brake system...
The proportioning valve is on the rear brakes only when the vehicle has rear Drum Brakes.
What it does is limits the brake line pressure to the rear brakes during normal stopping. This way the rear brakes don't lock up and cause the vehicle to fish tail or spin.
When you press the brakes harder than normal, the proportioning valve opens more to allow more line pressure so you're able to stop faster.

I’m happy to help further over the phone at https://www.6ya.com/expert/jason_00b31cc8f593773a

Booster problems are rare but they do go bad sometimes.
A bad booster generally causes the brake pedal to feel hard to push down, and a lot of pressure on the brake pedal is required to make the car stop.
Rarely, a vacuum brake booster will develop a vacuum leak, which can cause engine performance problems, hissing or whistling noise, as well as requiring increased pressure on the brake pedal to stop.

The first test:
With the vehicle parked, turned OFF, and the parking brake set, pump the brake pedal 5 to 6 times. If the pedal gets harder to push after several times, your booster is probably good.

The second test (To make sure):
After the test above, without making any changes, press and hold the brake pedal with light to moderate pressure.
Now with your foot still on the brake pedal, start the vehicle.
If the booster is good, you will feel the pedal go down when the engine starts.

Hope this helps!

Check your Brake Switch on the Back of your Brake Pedal, you have loose wires or your switch is not working properly

right calibration ??? no you need a proper mechanic here as what is wrong is the brakes need adjusting up on the automatic adjusters so the clearance between the shoe and the drum is minimised and this is a very skilled job so i would ask a local mechanic to do this for you .

Is the brake pedal getting harder to depress? Also have you had any work done on the vehicle immediately prior to this problem? If the pedal is getting harder to depress it could be a failing power brake booster if your car has one. Some ABS systems are different than others

It is , or you wouldn't need to press on the brake. Press harder.

You have to bleed it on all 4 wheel