Unfortunately that stand is totally unsuitable for use in a car - it has no way to secure the laptop, and has sharp edges. In the event of a crash,the laptop would fly around the car, and you could easily injure yourself or your passenger on the stand - especially if it got in the way of an airbag. A patio umbrella stand would be even worse, adding a heavy loose object to the mix!
I'd suggest getting a proper in car one that is type-approved by an appropriate safety body, which holds the laptop securely, and is positioned such that the screen isn't visible to the driver when the car is moving (e.g. angled towards the passenger) to avoid distraction.