I'm going to come at this from a different angle, with the caveat that the fiancée may well just be a horrible person.
However, she may not be. She may be frustrated with what she sees as difficult teenagers, and that her role in her own home is marginalised by being expected to have no say over what happens and how they behave.
I am the resident parent in your situation. I'm married to a woman but I don't think that changes the principles. DW and I started living together when my DC were 11 and 13, so about the same as your DH and fiancée. This is a tricky age to come into the lives of kids. You don't get the nice "kiddy" bit, it's the start of the teenage years. There's nothing "wrong" with my DC, they're normal teenagers. Like normal teenagers, often they are rude, particularly when being told things they don't like (like don't take your phone to bed, don't be rude when I ask you to do something). They did not take well to this new person adopting a parental role and telling them what to do.
Over the years this has caused some stress on many occasions - DW feeling that she has no power or control in her own home, me feeling stuck between wanting my DC to be happy and wanting DW to be happy.
I think that you also should acknowledge that even nice teenagers (which I'm sure yours are) will misrepresent accounts of what has happened to suit their own narrative. So what you hear isn't necessarily the unvarnished reality .
Ultimately this is between your ex and his fiancée to resolve, and the fiancée is going to have to do something hard to do, in trying to start fresh with your girls and acknowledge that while she isn't their parent, she is in a quasi-parental role and finds it difficult. Perhaps she has no kids of her own and no parenting experience before this.
Taking on someone else's teenagers is hard. Blended families are hard. It can work but everyone has to work at it, it can't be a war of attrition between the kids and the step-parent.
Obviously at 14 and 17, if they don't want to see their dad, they can't be forced to. That would be a real shame for all concerned and I'd encourage you to try to adopt a neutral position and not automatically accept everything your DDs say as gospel. Perhaps you can talk calmly to your DH and the fiancée about how you manage the situation together?