Clearly one of their six children was playing basketball, at a game. That child was later at the protest. The only reasonable explanation was the rest of the family was at the basketball game, and left together, getting caught up in the protest.
When ICE attacked their car, their story is they left their car, taking their baby with them, handed their baby to a bystander, and allowing other bystanders to remove their other children from the car. That would have meant they were among the protesters without their children.
Do you have evidence that the bystanders did not take their children out of the car? There does seem to be photos of their children out of the car.
Your window complaint makes no sense. If we believe their story, they would have rolled down their window to talk to the ICE agents. The made no statement about whether they rolled up the window after that, but it really does not matter. Tear gas under the car would be circulated into the car by the heating system. It was a cold day, so the car would have been sucking a lot of air in to heat it.