[Al Skierkiewicz]

Jacob,
The top two gates appear to be cross coupled and will act as a flip flop. i.e. change state whenever a new pulse comes in on the positive or negative input. (There is also a connection on the input to FET Q2 that I think is a mistake.) I am guessing that in the real device what you are looking at is a circuit that pulls down to ground when the negative lead goes open.

I think you can handle this with two simple inverters feeding one of the upper and lower FETs. When the + lead is positive, turn on one of the postive lead and one of the negative lead FETs. The - input lead is connected the same way. So the output of the inverter connected to the - lead goes high when that input closes to - and turns on a negative lead FET. When the signals reverse, the inverters change state and turns on the opposite FETs changing the direction on the motor. Effectively, this becomes a simple bridge switch. (think a diode bridge where the diodes are actually FETs) Design the circuit so that the negative lead FETs can both be turned on ( and the postive leads FETs will turn off) when both the + and - inputs go high and you will have the braking function.