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My truck sometimes pulls to the right when I'm stopping. Also, when I've been driving a little ways without using the brakes and then go to apply them I don't get much stopping power. But after that first push (to the floor usually) if I let the pedal come back up and then reapply I get good stopping power.
I replaced the front right brake hose to the caliper a few months ago, and it had new brakes and rotors maybe a coupla years ago. I replaced the right caliper before that (3 years+ ?) because I thought it was causing a shaky stop and pull to the right. It was an AutoZone brand so that may be a problem!
The pedal going to the floor says the master cylinder is bad. A couple of year is too long for the brakes - replace them. Shaking from braking is warped/bad rotors. Replace them at the same time.
Your 2WD is different, but look at the Brakes & Hubs album in my signature link.
First thing you need to do is make sure both calipers are working properly. That includes floating on the slides freely. I myself would replace hydraulic parts only in pairs. They both have the same amount of wear and tear on them, it only stands to reason that the old one will not function as well as the new one. Pulling to the right while braking would indicate that the left side is not working as well. Soft pedal can be caused be a variety of different factors, most common is a hydraulic leak, which also includes a leak in the seals inside the master cylinder. Poor adjustment in the rear brakes also provides a soft pedal. Last but not least , brake fluid is hygroscopic, which means it attracts moisture, which makes it "spongy". If the brake fluid is a dark color, I would recommend flushing it out and replacing with new fluid.
That was "floating on the slides" not sides. That is where the caliper mounts to the knuckle with the slide pins. The pins and the channels where they are inserted should be clean and lubed lightly with caliper grease to keep the caliper sliding without binding on the mounts.
BTW, you might think about replacing the left (or both) brake hose, since you replaced the one on the right. It's possible that the left hose is deteriorated and causing less force to be applied by the left caliper which could cause a pull to the right.
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