I feel that if this was the exPs time, and he had to work so the partner was looking after them, then this would still be a problem for you.
As a mum, step mum and a child of divorce, it is so important for the kids to bond with the new partner. It is so good that she wants to do this too. It is going to be hard this time for you, but you are creating problems for your kids if you prevent them bonding with her. They need to feel secure with her too and if you do stop this or since every time they mention her, it will become quite traumatic for them. They will feel stuck in the middle and start lying to either side.
You need to get your head around this for yourself, you have the children a majority of the time, allow this to happen for your children, and think about how much happier their time with their dad will be if they feel comfortable with his partner and how much more precious your time with them will be. She will never replace you and she won't want to. Don't let lines be drawn between yourself and your ex, because ultimately that could happen.
You have tonnes of time with your kids, please be happy this is happening and please see how lucky you are that your partner is not with some woman who hates kids and ruins his time with them, I have seen it and experienced it when I was a kid and it is scarring.