I think consistent boundaries and behavior on your part is best. Know that she may not like it, and may blow up at you.
I am not sure what I am supposed to do?
I'd just tell her that you are going with the kids and she is invited. Say something when you make plans. Say something in the morning when you are getting ready to go. Then tell her you are leaving.
If she txts you about wanting to go once you've left, either don't reply (when you are driving!), or just tell her that you aren't coming back for her now. Then spend your time out focused on your kids, not texting her.
Chasing after her, trying to convince her to go, and offering to turn around and get her is invalidating, rather than helpful. She is an adult; where they impact only her like this, let her make her own choices, and live with them.
Something I am concerned about, as well, is dBPDw has started having more run-ins with D14 and S12. Just about every time we go somewhere dBPDw ends up causing drama between her and D14 or S12. What is so frustrating is dBPDw gets to a certain point in the argument and then turns to me and asks why I am not backing her up or she will ask me if she is being ridiculous. I am supposed to answer that question sitting at table in front of our three kids? I believe in honesty but the few times I have told the truth, it was bad. Then I was accused of degrading her in front of the kids. She asked for goodness sakes. It is a tough situation to be in because D14 has asked me before why I don't intervene when dBPDw is acting out. Situations like this usually end with one of the kids crying and my wife in a hot rage.
I'd suggest two things. First, decide when dBPDw's treatment of the kids is over the limit for you. When this happens, remove the kid(s) from her.
Until this happens, try not to get in the middle of it. When your wife asks you a no-win question (back her up or say she's ridiculous), just say ":)on't ask me that." And stick to it.
You can later explain that she's put you in a no-win situation--you can speak the truth as you see it (which would undermine her, and you do not want to do). Or you can lie, which you won't do.