If they are in your home you are allowed to tell them off and correct their behaviour. If your partner is expecting you to take care of them then you can parent how you wish to. It’s also not your responsibility to have them whilst your partner is at work so make your voice heard next time.
Those kids are a victim of their parents circumstances. It sounds like your BD trusts you with them. Talk to him about the fact that you’re uncomfortable being in charge and that it’s really hard. Do not come from a place where you don’t want them around, come from a place you want him around. Ask him if he can take a little time off during the break to spend time with all of them. I grew up with a stepmom and a stepdad and they were both important people in my life. You are allowed to ask them to do things and to help you, and you can tattle on them to dad. They’re kids, you have to be the grown up and set your boundaries with them.
Well not having them around their siblings isn’t an option, but as a mom who has kids that have a step mom I’d be cool with her coming to me and being like hey I really don’t like the kids behavior towards me and I want to help us have a better relationship what do you suggest I do or what can I do to correct them. And also maybe she could talk to the kids who respecting you. For us all parents have the right to discipline our kids all equally.