those spikes are just noise. its not possible to tell where they are coming from without a lot of effort, perhaps equipment you can't afford, and the voltage ripple is directly proportional to the inductance between the three capacitors in your system, the capacitance and the resistance of those three capacitors, the 60 or 50hz frequency of your inverter, and the variable frequency of the alternator. by capacitors i mean your car battery, the super capacitors you have connected, and the capacitors inside the inverter.
the super capacitors should not affect the engine at all. if you have enough voltage ripple in your system that your engine's ecu can't hardly function, that's a very serious and legitamate possibility but unlikely to be the case. if that was the case your car battery would be unlikely to start the engine.
if the inverter puts out so much rfi and emi that your ecu is having trouble, also possibility, but unlikely that capacitors on the 12v dc side of things could stop it.
keep in mind that the car battery's impedance is relatively high in the neighborhood of 13 to 14 volts. the voltage ripple you saw might be entirely the voltage ripple generated by the alternator. there is litterally nothing to see here.
if the inverter is cross conducting you could see the kind of noise you're dealing with, is that 10 or so cycles in 200ns? could be cross conduction. this kind of noise is also generated by the ignition system and your car's ecu should be able to handle it