This is all so completely wrong - on several levels. I'd lay money on the fact that sooner or later SD will find out that her dad (and probably her mum) have been lying to her, and this will almost certainly affect her adversely.
A standin ...... oh FFS ! This is NOT about you wanting to play mummies, it's simply about you wanting to be a full and respected member of your partner's family. So far as SD is concerned, I get the impression that you'd simply like to meet the girl, be friendly to her and share her company every so often. It's about being considered important enough, in your DP's eyes, for him to actually admit you exist ....
.... that comment though, IMO, is very telling. What are the odds that the ex has put her foot down and demanded that you never meet SD because she does not want another woman to get anywhere remotely close to SD ? And DP of course, is being so bloody lily livered about all of this, that instead of turning round and telling the ex that he is an adult and quite capable of choosing the company his daughter keeps and the places she stays, he simply rolls over and then, takes all his frustration out on you.
FWIW, my partner has children, who, when he sees them, involves driving 400+ miles on a weekend to bring them back here (his ex won't share any part of the driving). There are a whole host of practical solutions he could employ which would avoid staying in a hotel (which, as Cappucino said before, is a totally false environment to see anyone in, especially a child). For example, instead of trying to see the child for a few days here and there, he could have her for a whole week or more during school holidays at his home.
I feel all this hotel/distance business is a smoke screen and that at the end of the day, it's not about convenience, it's certainly not about what's best for the child (especially as it's based on a lie), but all about what his ex dictates. How can he possibly believe, even if you didn't exist, that only ever seeing his daughter in a hotel is remotely "normal" ? It's even more abnormal to see her in those circumstances, with the ex in tow, and the 3 of them presumably going out together, eating together and so on. One thing you still haven't clarified is how exactly SD views this situation ...... does she know her parents are actually separated ? Even if she did, I bet she's hoping they're going to reconcile (naturally, if she sees her parents apparently getting on together) - and it doesn't look as though anyone is putting her straight on that (the "it would break her heart" comment) ..... and if on top of that she believes daddy is single, she's even more likely to hope her parents will get back together and they'll all live together happily ever after one day.
Boy oh boy .... this man is potentially storing up so much trouble for himself here. More importantly, his daughter could end up feeling betrayed if what she's always been led to believe isn't going to happen ....
.... which leads me to something else which troubles me about your situation. I apologise if the thought of this upsets you, but I can't help wondering if your partner is maybe harbouring thoughts of getting back with his ex one day himself ?
I also feel very sorry for his extended family who are also being prevented from seeing their granddaughte/neice. Have you ever been able to speak to any of them about all of this ? What do they think ? It seems extraordinary that once again (presumably) he is kowtowing to the ex's demands, resulting in all contact with the grandparents being cut. They must be terribly upset, because obviously the child must know they exist ?
I keep thinking about your story and I feel furious on your behalf. For him to swear at you like that was dreadful. You say you have experience of nobheads, well, in my book, someone who denied I existed and who swore at me when all I was trying to explain was that I wanted to be involved fully in his life - which he refuses to consider and/or make happen, is right up there on the nobhead scale. It is so demeaning and so horribly dismissive of you for him to be like this. YOU are the woman in his life now, he has chosen to be with YOU ..... yet his bloody ex takes precedence 101%. I can't think of a single reason why anyone would deserve to be treated so contemptuously and I'm sure you could do much better. I honestly feel that anyone living like this would end up having a nervous breakdown ...... could you really stand it for xxx more years ?
I know that previously I suggested counselling - I'm not so sure now. The more you say, I'm afraid that the impression I get of your DP is that of a cuckolded (by the ex) yet arrogant (towards you) selfish coward. Selfish ?? ........ yep, you are apparently "good enough" to provide adult company for him (with all that entails) and to ease his finances by sharing his bills, yet you are not "good enough" for him to introduce you to his daughter, nor does he value you enough to take the necessary steps to ensure continued contact with his daughter should his ex get nasty once you are admitted to.
My gut instinct is that he doesn't really want you in his life - not to that extent - and while I'm sure the ex is part of that, it also indicates to me that he doesn't view you as a serious/long-term proposition. And that, frankly, after 3 years together is extremely insulting and if I'm right, he's stringing you along, wasting your time.
I would get out. I couldn't be with anyone who didn't respect me. It wouldn't matter if he was a good conversationalist, good company, a good lover, witty, a charming dinner companion, someone who shared my interests and so on ...... if that same man also pretended I didn't exist when it suited him, I would feel there was something very fundamentally wrong. How dare he use you like this ?