No consumer car/SUV/truck that I've heard of has a battery/inverter combo with enough 120v power to run the standard wall-outlet Onewheel+ chargers which will consume over 200w. (It might exist, i'm just saying I've personally not found any >150w)
power cycling: the circuit is shutting down automatically, over and over because you're drawing too much current continuously. Cause damage to the onewheel? probably not but it will probably take forever to charge and could negatively impact your car battery.
I have the carvepower external battery DC charger setup, which uses a 120v charger that only draws about 170w (it takes a full 1.5+ hours to charge a 4.5Ah external battery). Today I'm going to try charging one of my external batteries with the outlet in my 2018 Equinox which has a stated max of 150w. I'm hoping I can find 20w of wiggle room. This would allow me to re-charge almost endlessly (until the gas tank is empty) off-the-grid!