OP I'm really sorry. Been there, done that, bought the tee-shirt. No other kids in either house in our scenario, and DSD lives with us, but the drama, threats, blocking etc are all so familiar.
DSD is now 18 so it's easier. She shares the crazy communications with her Dad or her friends but not me.
Threatening suicide is child abuse, child services are aware of that? In our case, years later, DSD still gets blamed for "destroying her relationship with her poor adoring mother" by talking to CS and she knows on one level this is bat$h!t but on another she still loves her Mum (but hasn't seen her in 6 months).
Your step child definitely needs therapy, and possibly family therapy with their Dad. A family therapist may invite Mum to partake but don't expect miracles on that front (DSD's Mum refused to engage once the therapist suggested she might be the problem, not DSD and her Dad).
It gets easier as they get older. Would it be possible for you to ask your DP to not keep you informed of the crazy? Honestly, part of me wants to know what's going on but my mental health is so much better since I don't. I mean if DSD comes to me for a cuddle I know something is up (she's 18) and DH will say "Oh, her Mum is blocking her again" or "Another poison pen letter arrived earlier" but I don't know the details.
Your DSC loves their Mum and wants her to be happy, but also loves their Dad and you and knows their Mum is the problem. This is such a horrible position for them to be in.
Over the years if we overhear calls between DSD and her Mum the tone is always placating but every now and again she'll errupt and it's always "Don't you talk about my Dad like that!" She's 18, she understands her Mum's opinion of her Dad concerns us not one iota, but she cannot stand to hear it.
If you need to move out, you need to move out. Living with the second hand crazy is so hard. Could you maybe try family therapy (for your DP and DSC to help them manage) and asking your DP to keep you in the dark (as far as possible) first?