I'm so sorry for all the comments on here. This is only the second comment I've ever posted but I have been watching your thread and I just have to comment.
Firstly, your daughter has to learn about money because even when she's older she's going to get a shock about how far money can stretch because clearly she has no idea. Show her how much you get paid, put a spreadsheet and show her how much bills are and how much you have to put away for x, y and z. I see you go on holidays every year which is completely fine but say to her I need to put x amount away a month so that we can go on holiday. Ask her would she rather have this holiday and have all these memories from this holiday or a double bed?
Second, she needs to grow up. Just because the characters on PLL have double beds that doesn't mean that she needs to have that as well. You don't have the circumstances that you can just give her everything that she wants. You offered her the front room, she declined that was her chance. To be honest, I noticed you offered her the double room which I assume is your room, you shouldn't have done that purely because she's going in a strop about it, your the adult, she's the child end off. You have sciatica you deserve the room, you pay the rent/mortgage she doesn't so just because she isn't happy that you all don't have what her friends have that doesn't mean that you should suffer. People are in a lot worse situations than what she is, this isn't the end of the world for her.
If I was you I'd offer to decorate the bedroom make it neutral, make it feel like a little more like a 'grown up' room, organise the wardrobe so she gets say 75% and the young one gets 25% and keep the young child's stuff in your room. Cut out the sleep overs because once the little one is in the room she shouldn't have to leave her bedroom just because she wants to have a friend over. Tell her she isn't getting a hot tub just because her friends one, after showing the bills tell her I only have x amount of money to spend on you at Christmas and that won't cover the price of a hot tub. I'd seriously start thinking about making her do chores and giving her pocket money, if she wants to buy make up, books, toys, etc then that has to come out of her own money and then she'll realise how far that actually goes and obviously you buy her school stuff for her or clothes in general but if she has a party to go to and she wants a nice new fancy top because her friends will look amazing she should be the one who buys it. I'm not saying you've done wrong but quite frankly she seems spoiled. I think your going to have to start putting your foot down because she needs to learn the value of money now and she needs to learn just because her friends have something that doesn't automatically mean that she should get that as well.
OP, I think you should consider about the future though, if you can't put up with this instead of living day to day, I know you don't have the circumstances right now to get a new house but you should maybe think about moving, I'm not saying right now or in a year from now but have a plan. If you need to save up start doing it now, budget yourself don't go away and spend money on expensive costs and shoes because quite frankly that doesn't seem like you daughter is appreciating that as much as she would all these other things she's harping on about.
Sorry to be so blunt. I really do apologise, I feel bad when people are saying about you having a second child but why shouldn't you have a second child?! I read your comment about how it's not like you have 6 living in a 3 bedroom but even if you did who cares?! You can have as many children as you want if you support them it has nothing to do with anyone else but your oldest needs to learn about the real world now because I'm sure it isn't easy for you being put under all of this stress.