How do we deal with this?

[Dumpylump]

How do you respond when dscs announce in every single argument that they're moving to other parents home?
Dsd is nearly 13 and getting moodier and more teenagey every day. She is often quite rude to dp (not me, funnily), and he doesn't always deal with it particularly well, so arguments can escalate out of almost nothing!
What dp is finding particularly hard to cope with, is "I hate you, I hate living here, I'm going to mums", and I don't know how to advise him. The only thing I've said, and I don't even know if its right, is don't say "ok then, go to your mums, I don't care", because he doesn't want her to do that, and he does care.
Anyone got any wise words?

Pandering to this sort of behaviour never works.
Saying I don't care wont work.
Saying something like "I'm really sorry you seem so unhappy, if you want to go to your mums that's fine" might work. ie empathise with them, let them go but leave the door open

She's very apologetic again this morning...didn't mean it, doesn't want to move to mums etc, etc.
I think dp just feels that every time she isn't getting her way, she's using this emotional blackmail. He really wants her there, and I think, because he told her how happy he is to be spending more time with her, and enjoys being a full time dad, she's seeing this as a kind of "hold" over him.

Can you all have a sit down when everyone is in a good mood and discuss this with your DSD. She may not realise quite how cutting her comments are. You could tell her that it is ok to argue and disagree (within reason) but threatening to leave is really quite a nasty thing to say.

Perhaps your DP could also promise to listen to her more or to be more consistant or whatever fits.

That's a good plan. I've tried before to explain to dp about letting small stuff go....will maybe have a chat with him again bout that, and then we can sit down with dsd and see what she says about it all.
They're both quick to rise to the bait if they're arguing (too similar!), but this one thing just is so hurtful to dp, and also, I worry that she might paint herself into a corner and end up going just to save face even though she doesn't really want to iykwim?