He definitely just turning the screws with the emotional abuse. What a tosser.
Reading this has left me with a "kicked in the stomach" feeling as it reminds me so much of my parent's break up.
Agree with PP that you need to stay strong and be prepared for it to get nastier. You absolutely need to keep it as clean as possible from your end, but without giving an inch on anything, ever. An old acquaintance of mine used to call it "showing the flash of steel in the spine".
I would also say if you can access counselling for your eldest DD, do that, sounds like she will need an outlet. And it also sounds like he is trying to use your daughter as a weapon against you. You need to shut that right down, because the biggest casualty in that will be your daughter.
The break up will bring up lots she has internalised around the lack of the relationship with her own dad. But all that stuff needs letting out, not stuffing back in the box. What she is saying now might be uncomfortable, but you know what, it is good that she is saying it not bottling it all up.
It is legitimate that she is upset and scared at this time. Your STBX is hijacking her feelings, telling her what is causing those feelings (even though it's not that, or not just that). It's a very effective emotional manipulation technique. If you can separate out those two things- her feelings and his gloss on them, you'll be in much healthier place.
As a suggestion, listen to what she is saying, acknowledge her feelings as legitimate. Try to get ahead of the curve on that by periodically actively asking her what is wrong if she seems even the slightest bit upset. Counselling would be good, if that's not accessible, a caring and impartial adult like a friendly teacher or older cousin/aunt/uncle could help. There will be good books for teens on this.
At 13, she will probably be old enough to start to understand what emotional abuse is. Gently educate her if you can. In a neutral way, above all by leading by example. This could become the reason she is able to avoid emotionally abusive men in her own future. It could also help her be a bit immune to the emotional abuse teenagers dole out to one another regularly. This can be a positive thing in the long run. She can begin to see through this type of behaviour much younger than most people do.
Don't let him turn her into a weapon against you and your resolve int he sort term. Don't let him turn your relationship with her sour in the medium or long term.
I hope someone can offer you good practical advice about getting him out of your home asap, sorry I don't know more about that. Women's Aid will.
Plus, I read somewhere, never accept a gift from someone who is abusive to you. It erodes your own self-esteem. It creates all kinds of blurry obligations and murky feelings. I started doing this with my SIL, who is low level abusive to a lot of people. Makes me feel a lot better. If it is impossible to give it back to him, then give it to an appropriate charity (e.g. local women's aid or refuge) so you are turning his energy against him.
in a similar spirit of turning his energy against him, if you feel at all unsafe, or that he is damaging your children you could sell it and use the money as an escape fund, but if you don't desperately need the money for practical escape reasons, get rid of the gift.
Good luck 