I have 2 daughters, a 12 year old and a 9 year old, I also have a 7 year old son. Is it illegal to have the 9 year old and the 7 year old share a room so that my 12 year old can have her own room? My girls don't want to share a room with each other and so I was trying to find a solution to my problem.

Unless you are being investigated by social services, there are no real laws ( often in poor families many kids will share one room)
But in this case no, while not a law, it is not really a good idea for older kids to be sharing, so keep girls in one room, boy in the other

No law but it would not be appropriate at these ages for the boy and girl to share a room. The solution is for your daughters not to think they get to tell their mother how the household will be set up. My sister and I shared a room at these ages. We didn't want to because we argued all the time. Whoever's voice was heard whining, crying or complaining or whomever was seen or noticed doing disrespectful or rude things to the other was up for extra chores. If my parents couldn't tell who was the guilty party, we both got extra chores. After a few months of dishes and laundry, we changed our tune and found a way to share our room. If we argued, we at least made darned sure our parents didn't know we were arguing!