I don't think she is spoilt or ungrateful: she is just entering an age, where peer pressure and peer comparison mean a lot. It doesn't even matter if you can say that there are teenagers and maybe even some of her classmates and friends, who live in either similar or even smaller houses. She will only see what she wants and can see from her own current standpoint.
The other thing to bear in mind is that teenagers need privacy and sharing a room with a 3 year old can be their idea of a nightmare. This isn't just about sleeping arrangements. I assume that sharing a room means that the 3-year old can come in there whenever she wants, keep her toys and other things there? Bear in mind that, in her own bedroom, your teenage daughter may want to keep items that she doesn't want to share with the 3-year old or, in fact, the 3-year old to see at all!
The only thing I can advise you to do is be open and honest about this and have an upfront adult conversation with her about the finances. Tell her exactly what you said to us here, i.e. that the home you have is the only one you can afford and that's unfortunately not going to change in the short term.
Before you have that chat, perhaps, there are compromises that can still be reached. For example, if the 3-year old sleeps with you anyway, then is it an option to move her bed into your bedroom? Is there an option to partition at least one of the bedrooms or another room to create 2 smaller spaces? Finally, is saving up for an extension an option? If the latter is an option, then one of the things to ask your teenage daughter is what sacrifices she would be prepared to make in the things she wants to allow you to save up for the extension?
It's all easier said than done, to be honest, OP, and there are no perfect or ideal answers. Teenagers are tough to deal with. I know that as I have one myself. But I still hope you can find a way to have an open adult conversation with your daughter. She needs to understand that money is at least one of the issues standing in the way of the solutions she is proposing to the separate bedroom problem and she needs to understand that not everybody earns the same amounts of money. She will then either continue complaining or will start thinking about motivating herself to study, get a job and move on. From that point, she will really get the answers as to what it takes to live in a house she wants in the area she considers desirable.