Full disclosure here...I am a landlord with multiple residential units. I don't know what state or local regulations that apply there. However, based on Colorado state law and my local laws, all of what you described could be perfectly legal here. I'm also assuming everything you described is legal and in compliance with the written lease.
If rent is going up 50% then I assume market conditions will actually support that. This might could be verified by calling around or asking some of the neighbors what their rent is.
If your friend has been a good tenant (i.e., paid on time, no neighbor complaints, no police calls, no damage to unit) then the best approach may be to explain to the landlord that she is having trouble finding a new place. Then ask for an extension of one month at the current rate. In return she promises to be out on time and leave the place clean and in good condition. That might buy her a little time to find a place and save her some money. From the landlord's point of view having a smooth turnover, with minimal vacancy, and no damage may outweigh getting extra $$$ for one month particularly for a good tenant. If she has been perceived as a trouble tenant then this probably won't work.
Between the rent increase and neighbor kids not playing with her kid then she is probably better off moving.