Her mums baby is 4 weeks old
And your mother died a month ago?
3months ago your mother would have been gravely sick (and I am very sorry about your loss I know what that feels like) and SD mother would have been heavily pregnant.
OH I can see what was going on in that girls life.. I suspect not a great deal of attention on her as everyone else was focused on so many other things. I suspect (rightly so) your dd would have had more attention too as people would know she was close to loosing her grandmother.
Phone the school for your sd arrange some counselling. Phone relate and arrange some couples counselling for you and your DP.
Dont throw out what you and your dp have because of a misguided girl who likely right now feels like nowhere is safe for her. She lashes out on your dd because she sees her as the one who has it all (her mum is likely very busy with a newborn baby and her new life - your dd has her mother all the time)
Send your op a text if you dont want to talk and tell him you will work it out but for tonight best you both sleep apart. Meet up for dinner or similar tomorrow and TALK thinks through.
Find a way to support everyone. You need a lot as you just lost your mother. your dd needs a lot as she just lost her grandmother and is watching her mother grieve. However your SD also needs a lot as a great deal of stuff has happened in her life. I am not keen on the phrase but I would say lovebomb her. Lots of attention and time.
You and OH have to find a way forward that works for everyone. means your SD has to feel she is cared for and means something to everyone.
Means your DD has to feel she has a safe place no one can go to.
Also means your OH has to feel ok about his home (he wasnt ok about the lock and you may say you were right as SD ruined your DDs room however that wont get any of you anywhere).
Personally I would get your SD to set her own punishment for ruining your DDs room. Tell her she has to make it realistic See what she comes up with.
Don't make her feel that if she messes up she looses people she loves.. Dont let a messed up and confused girl take away a relationship you 4 months ago would have said was a good one..