My Mum has been visiting family in the USA for 90 days from the UK; she has become too sick to return to England. How can we extend for 2 more months?
You should get the advice of an immigration law attorney. You will also need a paper from the doctor saying you are too sick to travel.
Medical emergencies are exceptions to the general bar on extending VWP status. U.S. Citizenship and Immigration Services (USCIS) can grant extensions of VWP stays, up to 30 days more, if you are hospitalized for an urgent matter or similar circumstances.
The catch is that you are expected to show up in person at a USCIS office, using an INFOPASS appointment. Such extension requests cannot be made by mail. That might not be possible for someone in genuinely dire health. The best bet is to hire an immigration attorney, who may be able to arrange matters on your behalf.
The next best bet is to save all records of your hospital stays so that, next time you request a U.S. visa or other entry, you will be able to provide proof that your overstay was due to circumstances beyond your control. It should not be held against you, assuming you leave the U.S. as soon as is reasonably, medically possible.
Thanks, @Andrew Lazarus for the link.