Another here who says snuggle away. I had 3 'normal' babies before my bundle of HN fractiousness. DH was exactly the same (and occasionally still is) but on the whole he's realised that if ds2 is happy, we're all happy
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I didn't find a stretchy wrap too hot last summer but I would wear it on it's own or just with a vest underneath.
Your DD needs you - she's been, to all intents and purposes, part of you for 9m and to be suddenly expected to be content alone in a strange world just doesn't suit some babies. Some it does - my other 3 were in their own room by 6w, sleeping through soon after that in 2 cases, but ds has truly broken the mould. He's still in our room, has slept better this week but until then has been a terrible sleeper. Still goes to sleep in my arms if I let him (though he self settles well too). Likes nothing better than a cuddle but is also independent. As I write this he's at the other end of the room, talking nonsense to the dog and putting his fingers up the dog's nose 
The difference between 9w and 13y is 12y43w. It's silly to base what dd will be like in 12y43w time on what she is now. I know we all say things in the heat of the moment, but really - its that silly. Your dd needs you and will grow to be an independent little terror darling just like ours, but I firmly believe that's because our babies were all given what they needed - unconditional, limitless love whenever it was needed try 24hrs a day!
That's not to say that it should always be you - having a HN baby is terribly wearing, so enlist helpful support wherever you can.
Also, for tea time fractiousness, unless you have a huge issue with them (I did but long since vanished!), might I suggest a dummy? DS wouldn't countenance a silicone one, but he loves his latex cherry shaped ones. In fact so much that he won't go up to the next size (who knew that dummies come in sizes?!) so we're stuck with Tommee Tippee bog standard latex ones. At least they're cheap! 
enyfshedd sorry for the essay but your situation really struck a chord!