I don't understand why she took on homeschooling if she is so chronically ill?
Four weeks out of school whilst totally incapable of providing an adequate education or supervision = Fair Access Panel referral.
And some muppets on shady sites delight in telling people that if they refuse a school place, IT'S THE LAW that the Local Authority can force the school of their choice to take them. Which it isn't - the LA can instruct a school to take them, but only if there isn't a place in another school - such as the one that had been allocated to RN in the first place, who wouldn't be allowed to remove her from their roll or even refer to the LA to ask them if she can be removed until another two weeks have passed, or any other school in the area that is undersubscribed. People of limited comprehension in admissions law love being told this, as it's what they want to hear, rather than 'Uh, no, keeping your kid away from other children, disrupting their education and socialisation doesn't guarantee them a place at the best school in the area with funding for taxis, it just means they get a place at the least popular one in the general area (which can be miles away).