So this is what you need to tell your wife. You need that space to provide for all of you while she essentially does nothing the majority of the day as your children are capable of taking care of themselves. If she believes your 16 year old daughter needs her own private bedroom, and that need is more important than the need you have as part of solely providing for all of your family, she can either start working to pay for the update or she can support you. She doesn't get to stay at home all day while the children are in school, and pretend she has an equal say in any of this. If it's that important to her, she should sacrifice.

Ignore the teenagers on reddit who think things should be given just because they're demanded.