How tomplement a Remote Control Trip Switch (circuit breaker) for 80-100A 12VDC

X10 is a good, reasonably inexpensive choice, whose standard has been around for a while, and thus has significant documentation and hobbyist examples available on the Internet.

For X10 projects/tutorials, you may want to start with this Instructable as well as this one.

Also, to learn more options, you may consider reading the book Smart Homes For Dummies, which provides background on a variety of options including X10, although this book is short on details for practical implementation.

That said, if you want to step the DIY aspect up a notch, you may want to invest your time learning to use an inexpensive hobbyist microcontroller board such as Arduino, and supplement it with some basic experiments with AC Relays. Then your options will really open up, including allowing wireless control networks, as well as power-on/offs triggered by sensor readings, status indicators, etc., limited by your creativity/requirements.

A direct connection is not a good idea since there are too many unknowns. The safest thing is to have the microcontroller activate something that acts like a switch. A relay definitely does this.

However, an opto-isolator will most likely work too, and will be smaller, cheaper, and take less power. You should be able to drive it from a microcontroller output with resistor in series. You don't need speed, so you can use a opto with decent gain, like 3x. 1 mA in yields 3 mA output current capability, which is likely a lot more than the switch has to handle. You still have to get the polarity right though. Measure the open circuit voltage across the button you want to simulate pressing. That will tell you which way around the opto output needs to be hooked up.