Seems as if your H only plays 'nice' when he's having a problem with S16, but when you are having a problem with D13 he uses it as a way to make things worse for you as a way to get her to live with him. This is the same thing he did with S16. Don't trust him when he's being pleasant to you. Your H is not going to show a united parental front unless it suits him to do so and he has something to gain (and you usually lose something). Your H's affection seems to be conditional.
I am glad that you and your D18 seem to be building a wonderful relationship. And here is the thing .... they will all leave eventually ... and they will all realise who was truly there for them. Here is something else to consider (if D13 does go live with your H) .... she is coming to the age when you and her will spend very little time together. You've seen this with D18 and S16. This is not because they are avoiding you. It's because they are starting to pull away from parents, separating and finding their own way. My D16 and I have a fantastic R (which I'm sure you have when things aren't heated and difficult with your H), but if I see her an hour over the weekend it's a lot. After school, perhaps 20 minutes or so, then she's off to her activities. This has been the sitch since she was about your D13's age. My S21 was the same around that age, even left home at 18 with his twin sister, but he's back and around us all the time. He' such fun. He even brings his friends to hang out.
So, why am I telling you all this ... to show you there's hope. Don't 'beg' them to keep you company and when they are around you, have fun (show them your humorous side), while still enforcing your rules. If there are boys in the bedroom, go sit there and engage them in some funny conversation ("oh, hi, didn't know we had company") and then say perhaps something like, "well, it's been nice chatting, but we'll have to continue downstairs as you probably know." IOW, make D13's friends feel welcome in your home, but out of her bedroom. Get to know her friends, their parents, other siblings, their stories. Let them talk to you. Have stuff they can play with at your home ... shuffle board, tv games (outside her bedroom, of course). Feed them ... always have stuff in the 'fridge that they can nosh on ... give them freedom to do so (it's worth it to have a teen boy rummaging in your 'fridge for leftover pizza during a game) and your D13 is at home. Who knows, S16 may find things more attractive at your house. We have even invited D's friends parents to our house for BBQ's, so that may be something to try. We, of course, had boundaries and rules. We went down to their hang-out place, and one of the friend's was necking with another and I felt perfectly comfortable with telling them that no face sucking was allowed and we prefer there be some space between the bods (and it was my daughter who told us to come down ... weird).
I found humour goes a heck of a long way with teens. The things I used to tell my kid's friends. Oi!!! You know the score, you've been there .... you are the adult and you must know how to manipulate them without making them mad. That's exactly what your H is doing, I bet. Omigosh! I remember smiling at one of my daughters and saying, "aw, you're so cute when you're mad ... come give me a hug ... come on, you know you do." Ha ha! Then I would giggle every time she flipped her hair in annoyance at me and give me the ol' 'ugh'. She was so hilarious. I did get really cross sometimes, though. My H worked away from home for several years, so it all hung on me because on the weekends I didn't want any blow-ups while H was at home. Well, that daughter is just so wonderful now and we are close even though a long way from each other.
Anyway, this is my opinion, for what it's worth. I am no expert. I think I was just lucky and I also had my H, so that is a plus for me. Just keep calm, be subtle about this, don't ask or beg your H for anything (not even help with keeping a united front). You can do this, ACJ. Good luck!!!!
Me:57 H:52 M:28 Got another lawyer last year and filed. D35,S/D twins28,D22 EA4/04 End? Who knows? "Life is like a mirror. Smile at it and it smiles back at you." — Peace Pilgrim