I'm thinking that it very well could be one of two causes: a malfunctioning ABS modulator, or a malfunctioning Vehicle Speed Sensor. Either of those can cause your ABS to kick on and off, especially since you've had issues with the pedal fluctuating when you go to brake. Also, check the gear ring where the VSS is, and make sure those are in good condition; if there are any missing teeth, replace them.
The last thing would be, check your brake fluid. If the color isn't clear, check it with a Digitial Volt/Ohm Meter (DVOM). Set the DVOM to millivolts or volts (depends on the model, but it will say if the range can be selected or not; some DVOMs do the range automatically). Next, take one of the probes and put it into the brake fluid, and the other on the master cylinder casing; if the reading you get is 0.3 volts or higher, flush your brake fluid. The reason why you would have voltage in your brake fluid is because water still, through heating and cooling, condenses on the inside of the lines. If your fluid is bad, it won't hold pressure.
Also, make sure there is no air in your lines either. Hope this helps.