Hey RC, I'm sorry to hear the bad news. I hope your sister and niece don't face any worse medical complications than what they are already facing.
Does your sister understand the importance of cycling an ice pack on and off her swollen hand? I am not a doctor, so I am not qualified to give medical advice. With that said, the advice that has often been given to me is to apply ice for 15 or 20 minutes, followed by the same amount of off time. Repeat many times, starting as soon as possible following the injury.
I have also heard that applying heat during the off times can be good, so you are cycling heat and ice, but the first and last cycles should be ice. Do the whole process two or three times a day.
You can make an ice pack by filling a plastic freezer bag two-thirds with water and one-third with isopropyl alcohol. Toss it in the freezer, and it won't freeze into a solid block of ice. When I do this, I double-bag the ice-pack, just in case I get a leak.
If your doctor agrees, taking a maximum dosage of Ibuprofen for a couple of days may also be appropriate. That's 600 mg three or four times daily. 2400 mg.is the maximum daily dose.
Ice and Ibuprofen are good ways to reduce inflammation and swelling.
The other thing she should do is keep the arm elevated, at the same height as her heart. This makes it easy for blood to flow in and out of her hand. So lying in bed qualifies.When seated, she should rest her arm on a table if possible. Stack up some pillows, if that helps.
Once again, it is important not to delay. She needs to start elevating her arm now, not tomorrow.
Good luck with this.