The DC to DC laptop car adapters are significantly more efficient than using an inverter to power the original power brick which came with the laptop.
That original power brick takes 115vac and converts it to 18-19.5vDC.
Your inverter is taking your battery voltage 12.x vDC to 115vAC, and then the power brick is reconverting it back to 18-19.5vdc
Double conversion= more losses.
The inverter giving up is likely due to too thin of wiring to the ciggy plug receptacle. This is common. When I first got an inverter back in 2001, it could not power my laptop from a rear ciggy plug receptacle, but could from the one on my dashboard.
The problem is the wiring. It is too long and too thin and when the laptop places a load on the wiring, it has too much resistance, causes the voltage to drop too far and the inverter cannot work.
When the voltage drops, the amperage the power brick pulls increases, causing even more voltage drop.
Ciggy plugs are problematic themselves, even if the wiring to them is sufficient. They rely on spring loaded steel contacts both on the Nipple(+) and the sides(-). These contacts are usually steel, which is not a great conductor. When the current the device asks for is great, these contacts heat up greatly. Eventually the springs lose their spring. They can even melt the plastic that houses them.
Ciggy plugs and receptacles are a ubiquitous connector, but they are a poor connector, that wastes electricity by heating the wiring and contacts on connections. One can improve their devices with higher quality receptacles and plugs, but the basic issues are not eliminated.
Here is a BlueSeas plug and receptacle I bought for my laptop power supply, but I have never put it into use.
This plug kind of locks in place in the receptacle:
The OP can choose to rewire their existing ciggy receptacles and eliminate the issues of the inverter getting too low a voltage. 12 awg wire can be used, and it should be fused within 7 inches of the battery terminals.
I have many Ciggy receptacles, but only ask them to pass around 1 amp. My laptop can draw upto 8.5, and this was too much for the Ciggy plugs.
I use Anderson powerpoles in the 45 amp flavor for all my connectors now, and am Phasing out the SAE 12v connectors I originally used.
A DC to DC car adapter for the chromebook might also eliminate the issue.
And while the large battery in the Van might look impressive, most people Assume that the alternator is a magical near instant battery recharger, but this is false. It is quite easy to deplete a battery, and replacing what was taken takes much much longer than most people think.
Getting a battery from 80% to 100% takes about 4 hours, no matter how powerful the charging source, and when a battery is under 80% charged, it is degrading. The lower it rests and the longer it rests there, the more it is degraded, and the harder it is to return it to its maximum remaining capacity, which is not the same at its capacity when new.
I have devices that measure amp consumption. Last night I streamed 3 Movies on my laptop. It consumed 47.98Amp hours from my 130 AH battery, which is likely now only a 85 amp hour battery after ~460 cycles and mostly prompt and proper recharging.
A starting battery would never last 460 cycles depleted to 50% or more even if recharged promptly and fully after each discharge.
The largest battery which can fit in an engine compartment on a Van is likely 100 to 115AH. So while it might appear impressive in size weight and price to replace, it does not store that much energy. My laptop alone could deplete such a battery to ~50% just streaming 3 movies.
So the Combination of too thin of wiring to the ciggy receptacle, the poor nature of the contacts of ciggy plug and receptacle, the double conversion losses, and battery degradation due to chronic undercharging, all contribute to this ciggy plug inverter not being able to properly power even the chromebook's lesser electrical demands, compared to other laptops.
