@LP9,
My suggestions for what they are worth: Which could be nothing!
I think the first thing that needs to happen is you and your partner have a very big discussion about your role with her kids.
You need an agreement about this and you need to be working together.
You clearly disagree about discipline and I, having been a step parent and having worked with lots of them, don't think you just muscle in and act like a dad without prior agreement.
As an adult in your home and as your partner's....er partner, you clearly have some rights and responsibilities and hence some degree of say. However, you are not the dad or the mum and your role needs to be negotiated.
I agree with Bobsal that there need to be consequences but if you and the mum are not on the same page and you act alone there is going to be all kinds of trouble.
The kids also need to be consulted and an agreed upon role negotiated for you.
If you and your partner cannot agree upon a basic co-parenting and discipline framework, I'd suggest going and getting help to work one out.