Send the general health form and confirm it needs to return to you, you then meet before you can confirm if her daughter can start. Unacceptable telling you to Google information, even professionals specialising in the condition need specific details about day to day presentation. You need to understand and see if possible to mitigate any implications for the unit - ratio, planning, activities, risk assessment and leader allocation.
Mum needs to understand from the start that it's a partnership, not respite. If she's being like this now I'd get the division or county needs advisor and DC involved now and have a clear audit trail for all communication.
Consider: your current ratios, do you have enough volunteers to cover if one of you is on holiday or having a bad week at work, will district step up to help if you're stuck, will the other children in the unit be able to have a safe and enjoyable time, current sen demands on the unit and do all the volunteers feel able to manage if other girls.have existing considerations.
For my unit when thinking about additional needs, do you trust the parents, will they respect you and the team, do all the vols buy in? When we have proper dialogue with parents and trust they tell us everything or we can ask questions AND leaders don't feel overwhelmed or put upon it works even with multiple girls with needs.
Please remember that even squeezing in just one more Rainbow, if you are not confident you will be able to properly support the girl due to complexities, volunteer ratio, lack of information or can't work with the parent you absolutely do not have to accept her.