What's the best way to use a switch to launch a minecart that's held by an unpowered booster, and then have the booster reset by passing over a detector track?
I'm unclear on quite what you want (and why a button, which will activate the booster for a short period, is not adequate) but it sounds like you want to use an RS flip flop. "S" input from whatever triggers your booster, "R" input from the detector track, output to the booster. Look up RS flip flop in the minecraft wiki redstone circuits.
Minecart track circuitry question