I'd tell him the truth - he is fucking his own child up because her making him feel good is his priority, and not making her a likeable, responsible adult when she leaves home. He is also damaging her relationship with her own mother, because she loses respect for you and you lose affection for her, and finally, he is threatening your marriage, which should be a huge issue for him in its own right but is also something that threatens the children's wellbeing, too. All because he likes his DD giving him cuddles and snuggles instead of childhood hissy fits. To be blunt, he's being selfish and pathetic.
Please don't be angry with her - I know it's impossible to feel warm and fuzzy when your kid does what she is, but he is letting her down far, far more than anyone else in this situation. She's not getting the help all kids need in managing their own behaviour and emotions, and in learning nasty behaviour has consequences - especially when aimed at someone with authority over you, if we're talking practicalities rather than ethics! Finally, it's part of the problem that he is damaging her bond with you with this bullshit. That's very toxic for her. You're her mum and she is still very small.
I don't think his defensiveness is actually your problem at this point. It sounds as though past nicey gentle approaches from you have changed fuck all. So be blunt. Tell him he is fucking up his daughter because he enjoys the ego strokes of being hero Daddy more than he loves her - none of us like being the bad guy and disciplining but we love our kids more than we like feeling good - that he is fucking up her relationship with you by making you so easily dismissed and creating contempt on her side and resentment on yours - and that he is fucking up the marriage because of his behaviour, too. He needs to work out what matters most: his ego, or his family.
This behaviour isn't because he is weak. It's because he is selfish.
In your shoes I would be insisting that:
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she is called down to talk to you both, but he does the actual talking. He needs to say he had no idea she was deliberately being so horrible to Mummy, that she is very shocked and very sad and disappointed to know she could do that, and that he has decided she is to have no swimming or other treats for the next two weeks, and if she does not start treating you with more respect, they will not start until she does. He also needs to say she is on a total screen ban until she gives you a courteous apology.
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He has to do a parenting course. No ifs, buts or ands. He is fucking your kids up.
You have to go in guns blazing, IMO, focusing on how badly he is letting your DD down - not you, as you are a grown woman and can look after your own interests and can always, if things get bad enough, leave - but the child who is totally dependant upon you both for literally everything that leads her to a happy, independent adult life. He is failing her. He can try to gussy it up however he likes, but it's putting lipstick on a pig. The truth is, he enjoys feeling like he's her special Daddy and she's his special girl. And being the bad guy as he says no/calls her on bad behaviour doesn't reward him emotionally. He's exacting his emotional needs from her and at her expense and welfare. That's really, really shitty behaviour and it has to stop.