There's a lot of background information coming out here, O/P.
I've been in your daughters position with the anger, from around the age 14 onwards when my Mum met my step-dad, but they never had any children together.
I was really angry and jealous about this relationship. I never knew my real Dad. Unfortunately, you're her nearest and dearest which means you're the one she is going to lash out at and hurt. It's not condoning it, but it's clarity on why she is doing it.
Her dad was abusive to her Mum
He went to prison
Mum met someone else
Mum had another baby
Dad died
That's been your eldest daughter's life. She shouldn't have had to go through any of that. She's still a teenager processing a lot of traumatic and confusing feelings. She's probably feeling rock-bottom and needs anger management lessons, and coping mechanisms. At the same time (I'm a counsellor) - I'm not making any diagnosis - It sounds like she needs to be assessed for cognitive disabilities and mental health illness. Aggression can be BPD, Bi-polar, schizophrenia, Autsim/Aspergers, Anxiety, Stress, OCD. A combination of many things.
When I was her age, I would also call my Mother many awful things, but my parents were also abusive toward me when dynamics changed.
I know it's easy to say, 'Don't award her bad behaviour with a holiday', but it's not really bad behaviour - It's mental health issues manifesting in lashing out. She's hopefully not taking any drugs (weed can also cause aggression in some people), she's not stealing, being physically violent, not damaging anything? It's just the verbal abuse?
Take her on holiday and every time she lashes our, pull her into a tight hug and tell her you love her. Keep doing it. Fight for her because she needs someone to fight for her, to hold her up while she self-destructs. It's going to be hard work and you're going to want to snap at her, but don't. Stay calm, be Mum. Fight for her.