OP I think there are many issues conflated in this post.
I don't think its unreasonable for a 13 year old to have a bedtime on a school night (less so on a weekend) but at 13 that's not going to be as early as you might like (10pm maybe?) and therefore isn't going to buy you much alone time if you go to bed at 10.15. If you really feel like its important for your wellbeing to have some time sat watching a TV programme without her, could you stay up later than this? If not, then I'm sorry but your Dd really can't be punished for that. Could you put a TV in your bedroom so you could go and watch something on your own? (But if you do this I think you need to be careful to keep it an occasional thing and not for it to turn into a place you go to avoid dealing with the deeper problem)
This is a normal stage of adolescence and your resentment towards your daughter for what is normal behaviour is palpable. I really think you need some help with this and I would suggest some counselling. That resentment seems to be at the core of everything and unless you address it, I suspect that anything else I or anybody else suggests is going to really be tweaking at the edges. Also your DD is going to feel it and is that really what you want?
If you need some time on your own, that's understandable but banishing your daughter (on a regular basis) isn't ok - especially when she can't go to her own room (expecting her to sit in your room really isn't fair). Could you go and sit in another room and read a book, or do a jigsaw or something for a bit? Could you go out for a walk? Do you have any hobbies that you do an evening (or a couple of evenings) a week? Even meeting a friend for a walk twice a week might help.
I get that there's stuff you want to watch on TV that might not be suitable for - I'm a mother of teenagers and I hear you - but I'm afraid that's just one of the sacrifices of parenthood. I remember when my kids were babies I couldn't keep up with TV programmes as I was too knackered, then bedtime routine (and DC that wouldn't sleep) got in the way, then it was evenings full of taxiiing kids to hobbies. Now it's that the programmes I want to watch might not be suitable (my oldest is actually 16 and is now in the next phase where what she wants to watch isn't suitable for me
) I'm afraid this is just part of parenthood. Eventually (I'm told!) they move out and we get control of the TV back!
Can you plan nice things to do together in the evening? Are there TV programmes or films you can all watch? Could you play board games? Does your daughter have any hobbies - if so could your DH take her, so you get an hour on your own? Is there a hobby you and your DD could develop together as your "thing" -not every night necessarily but just some positive time you could spend together? Or a TV programme you could get into together?
The crisp-eating and glasses-fiddling.... it's really hard to tell how reasonable you are being from a post. My teens can be incredibly annoying to watch TV with at times (and I've once paused a TV programme until one of them had finished their incredibly noisy eating that was annoying the whole family) but this is easily stopped with a "can you stop that". And I have to admit that I think the obvious resentment towards your daughter does make it sound as though that is tainting your reactions towards what sounds to be (at worst) normally annoying teenage behaviour. What isn't reasonable is for you to turn the TV off and end the night for everyone because of it - that's a complete over-reaction.
You also sound resentful that your DD is cuddling with her dad, and I wondered if this really about other issues in your marriage? Do you feel your DH doesn't give you enough attention or affection? If do then I think this is something you need to discuss with him separately rather than projecting this onto your DD. If you arent getting much attention/affection from your DH then asking him to address this is reasonable; expecting him to stop giving his daughter affection/attention isn't reasonable.
From your post it sounds like you don't think your DH will back you with your DD and I wonder whether he also senses your resentment towards her and is defensive of her? If so, I think this again emphasises the importance of getting some help with this.
I'm sorry this has been so long but I hope it's been some help.