I think there's two issues here with the OP.


First one, it doesn't seem that the mother has clear boundaries with the kid on who the parent in the house is. The child hasn't learned the skills needed on how she handles her own bad moods. Refusal to get out of the car is basically a temper tantrum. Temper tantrums should have been nipped in the bud after the first one occured at what... 2 years of age?


Second one, without knowing the history of the OP this is only a guess. If a dating parent is continuously bringing new and different people around the children/the house and expecting the children to just accept that, enjoy that, fall into line with that, then any problems or negative feelings the kid has about it are going to be magnified. The child's needs and wants probably weren't taken into consideration. They're just expected to automatically like and immediately get along with the new 'date'. That's going to result in resentment, which will result in acting out.