That's exactly what I am talking about. We can put the ex behind us and move on, but because we place so much value in our kids and make it known we will do whatever is needed, whenever it is needed, for their behalf, the ex can use that to make our lives miserable.
My ex knows I will, within reason, drop everything for my kids. If I have nothing else planned, I will always be willing to take them on short notice. I will do this for them, while my xW will abuse this to suit her own selfish ends. Still, I have never complained to her, even when it has meant some inconvenience for me at times.
(And this has resulted in xW now taking the opposite tact, in denying me such extra time with the kids by letting OM watch them instead. Just to spite me. Like you said, beeyatch!)
I don't know what the terms are in your parenting agreement/settlement, but many contain stipulations for who is responsible for transporting the kids and when for exchanges. My PA doesn't really contain enough wording to cover our sitch, so I just assume I will make the trip to/from her place (or her mother's) whether I am picking up or dropping off.
I think your ex needs to move her butt and get the kids to you if that's her responsibility during drop-offs.