"W asked if she could have lunch with guy, and come home a little later. I begrudgingly granted her this, thinking this might push back her time to 4 or 4:30."
Not sure if it would have helped in this situation, but as a general rule get all the details out in the open so that you know you're on the same page. If she says "a little later," you say, "So, then I can expect you home at 4 or 4:30, is that right?" At least get a firm commitment from her.
When she called about the car problems, I would recommend asking her straight out: "When, then, can I expect you to be home?" It isn't fair for you to just have to sit waiting (babysitting the kids), not knowing when to expect her.
Now, as for what really happened, we can't say. Were there really car problems? Was it just an alibi? Could it have really taken 3 hours to fix? Well, the answer is, maybe, or maybe not.
At some point you could ask her why it took 3 hours. At that point, you'd have to decide whether to trust whatever answer she gave.
It's understandable that you were upset. Your day did not go well. It's also fair enough (IMO) that you went out to eat alone. Doing so may have staved off a loud argument.
Eventually, you may want to talk to her, about how the day went from your point of view. You kept on having to make bigger and bigger concessions. Now, maybe her day went badly too, but she'll have to speak for herself about that.
This will probably continue for some time, this series of jagged ups and downs. There will be some days when she treats you right. Other days, she will neglect you. She is still letting the NRE cloud her judgment, and I suspect she is (perhaps subconsciously) rebelling against an array of regrets. You are getting caught in the whirlwind of her rebellion. It will take a lot of patience to get through this.
Make sure you explain to your counsellor that you are very frustrated with the situation right now. Make new decisions about your boundaries if you need to.