I recently bought my mustang used and the brakes look like they've never been touched. All rotors were under spec and the pads were almost gone. I replaced everything and took off the rear calipers to clean and reassemble them because the pistons wouldn't screw down at first. Once i got them working i put them back on and bled the brakes. The first time i bled it they were really soft so i waited and drove a bit and bled them again, it made the brakes stiffen up but they still feel like they are lacking and a little spongy when i put my foot down at first. I heard the problem might be air in the ABS which i hope isn't the case because then i have to pay the ford dealer 50 bucks or so to bleed that

Also, whenever i brake hard to the point of ABS turning on, it seems like one side locks and releases then the other side locks and releases making the car shake and i don't think the ABS is supposed to do that, but i never tested the ABS before i did the brake job so i don't know if the brakes just need more breaking in or if its because there's air in my abs lines or what. Can somebody give some light to my situation?