What are the ages of the children?
If she is depressed and has other issues, she should not be driving anywhere.
No reasonable person takes the time to properly install carseats each time they go out. It is extremely time consuming to do it correctly.
Nowhere does it state they have more than one car. Most people have carseats for each of their vehicles or if it is an infant seat, they do not need a snap in base for all since most can be belted directly in and the child is usually loaded into the carseat in the house.
If she were going to take the children, it was irresponsible of her not to let the children's father know where they are and to a;llow him to speak with them. If she is that depressed, she is a danger to herself and them. If she were that stressed, her parents should have gone to her house to assist in the care of the children rather than remove the children from their home. They are not HER children alone.