Chris,
The sound shaping functions always occur before the volume pot. You can take the signal "after" the volume pot if you think you can figure out which lead goes where. Keep in mind that some volume pots have a lot of leads (as many as 8) which may include loudness compensation circuits too. From the volume pot, the signal almost always travels through a 1-uf coupling capacitor. Whether or not your new amp setup requires this will depend upon how your amp is configured. This capacitor is important to block DC signals from reaching the amp input. It also helps prevent cascade failures of the system if the preamp malfunctions. Some amps setup also includes a series resistor in the signal path. This is more to prevent the preamp signal from getting loaded and dragged down than to attenuate the signal. A proper attenuation technique uses a voltage divider setup. A series resistor is not that so don't be afraid of including it. Somewhere around 8.2k to 10k might help if you are experiencing some distortion attributed to loading of the preamp. Premade amps, like car amps, usually are designed to operate on line-level signals. The internal signals that power the internal amp is not necessary match standard line-level specifications.
Speaking of, keep in mind that these circuits are all engineered with the factory internal amp in mind. Impedance matching is the issue here. The output impedance of the preamplifier is designed with the factory amplifier input impedance in mind. Tapping into this signal alters this balance and can result in poor performance, perhaps manifest as distortion, hum, etc. If both the internal amp and new amp circuit taps this circuit, then the impedance has been effectively halved (varies depending upon the input impedance of both amps). If you look at the circuit diagrams of your boombox, you might even find resistors tethering the input signal path to ground. While the resistors might have high resistance (30k +), it is still an alternate path to ground and reduces impedance. Tying another new circuit to this orig circuit affects the original circuit in what way then? Don't know? Neither do I. It depends. Bottom line is that while it sounds simple, the truth is that it's usually not quite that simple in real life.
It is worth a try though. However, if you find that the results aren't what you expected, you may have to consider experimenting with adding a series resistor, or divorcing the orig amp from the circuit to reduce amplifier input impedance. Since most volume pots are soldered directly onto a PCB, this might not be as easy as it sounds and could involve cutting PCB traces to do. However when adding a second amp adversely affects the impedance balance and you are getting poor output, this might need to be done since the old circuitry is acting like a drain and doing nothing but going along for the ride anyhow. Removing the old amp chip alone won't do it, since there are appurtenant amp circuitry that will affect impedance. Also keep in mind that when replacing an amp like this, the original spatial sound features will usually no longer work. To reactivate, the circuit will need to be redesigned or modified.
. 
)
