I don't really believe in toxic people. Everyone has good and bad in them. It's just whether the good is worth the bad IYSWIM? I think you need to set some boundaries, her strop and following around in the car is not acceptable, nor is her undermining you as a parent or constantly criticising you. Does she have mental health issues?
Of course, if this is having a big impact on you where you feel like you can't bounce back from these comments, and that it is causing you too much upset and distress, it is always acceptable to go Low Contact or no contact, whether the person is family or otherwise. Nobody is entitled to a relationship with anyone else. Even parents do not have a right to a relationship with their children, their responsibilities always come first. If they cannot be responsible then they lose those rights. We do not have to spend time with anyone who is detrimental to our mental health.
Really you need to work out whether you want a relationship with her, how much of a relationship and set your own terms. It may be that whole days out are too much, whereas an hour or two goes much better (say at the local park or for a coffee, somewhere you can make a get away if things get tricky!)
I absolutely love my mum and spending time with her, but we argue sometimes when she feels taken for granted and I feel got at. She thinks she's being helpful, I think she's being critical. There is also a lot of issues in the past where even though we can talk about it sometimes there are still negative feelings that come up. Then there is the disagreeing about how I parent my kids, and when she thinks I'm criticising how she parented. There are always going to be those issues.
But if it is a pattern of emotional abuse where she is eroding your sense of self esteem, gas lighting and manipulating you that's different. Do you think she's being emotionally abusive? Or just insensitive/thoughtless?