I completely agree with you, IMO why should you be ok with another woman pretending to do your role. I have DD who is 2 and recently referred to X's GF as Mommy and her name attached. Even though this bothered me I corrected her gently by repeating GF name. I did not make a big deal about it although it bothered me, I also realize even though I dislike this woman for my DD to look at her in a mother way is good that means this woman is taking care of her. In your case though the kids are old enough to know the difference and should not be told what to call there SM. Her name is good enough or would she rather be called Step Mother LOL. What is wrong with some SM. I have been in the SM position and never wanted to cross the line, I respected BM and she respected me. We never had issues. In fact till this day we are still great friends even though I am no longer with SD Father. Some women completely amaze me!
the date thing maybe just a coincidence thing, I would not even think twice about it. Don't give them the satisfaction of thinking you are Jealous.