Why am I getting negative voltage on MOSFET gate?
The control of your MOSFETs relies on a gate voltage with respect to source. M1's internal diode will never be forward biased by BAT but, M2's internal diode can easily become forward biased when ALT spikes low. I guess it's an alternator that ALT stands for so you can expect a lot of spikey stuff going on.
This question was answered before the OP disclosed that: -


  The alternator is currently not connected.


If the ALT is not connected then the sources will float and the circuit cannot be expected to do anything sensible. To user95482301 please don't keep editing the question without thought to answers that are already given. If you have to edit-in new information then please do it at the end of the question so that someone doesn't think I'm a moron for not reading the question correctly. Make it clear that new information is seen as new information!

Back to the original answer and it is still valid should the OP decide to connect the alternator: - 

So, ALT spikes low and M1's source source follows it. Now, due to capacitance between gate and source (8 nF), that pulse transfers to the gate and maybe your driver can't do anything about that negative going spike because once it happens, there's a chance that Q24 is dead.

BTW I wouldn't use a 30 volt rated MOSFET in an alternator circuit. When that spike arrives from the ALT net, M1 will see +12 V on BAT and -25 V on its source and that exceeds the DS rating by 7 volts. It might survive a while but don't expect it to survive long-term.