I'd say that before you give permission for your dd to take part in these tasks, you need to see the risk assessment that has been done for each of the tasks for a 'typical' student and the ones that have been done for your child in light of her medical issues that reduce her ability to do certain things. And that you need to see both so that you can see what additional adjustments have been made for your child over and above the rest of the class. And that due to the special medical needs your dd has, and how the teacher has already demonstrated to you when discussing this that she has not understood your dd's needs, you consider it a safeguarding issue that they are ignoring the welfare of your dd if they make her do these things - and that you will take the issue further if they continue to make her do these tasks without providing the requested risk assessments (because although other tasks may be more suited to her needs why should you take their word for it without them providing any proof, when they've been dismissing your concerns despite you knowing it is an issue).
Obviously if you phrase it correctly it will sound like you are willing to let her do the tasks once you have seen the risk assessments - and the sooner the school provides the risk assessments then you'll be able to check that they have done them correctly for your dd, so until that point it is the school that is causing the hold up rather than you.
I'm hoping that the school has at least done risk assessments for the general pupils rather than the special cases. Obviously I'm hoping that they have also done them for pupils with specific needs that could be impacted by these tasks. If they haven't done them then with it being SATS time of year they may well not want the bother of doing them and delay so your dd gets away with not doing anything. If they haven't done them then I'd be kicking up merry hell too as WTF are they doing something like this without doing them?!?
It sounds like the teacher has no understanding of your dd's condition and its effects - not to mention the long term implications of doing things that she shouldn't do. So it sounds like any risk assessment they have done for her will need you to improve it quite considerably... Which is your chance to both educate the teachers about your dd's problems and to show how it is completely inappropriate for her to be doing the task she was originally set to do for 6 weeks (and any others if that's the case).
Sorry if I sound a bit strident. I have a friend who has EDS (a severe form of hypermobility) who has ended up in a wheelchair as when she was at school she didn't know she had the condition, and sports teachers just thought she was being lazy or not trying hard enough so made her do lots of stuff that would have been fine if she had not had EDS but caused her condition to get a lot more severe a lot more quickly than it should have done. So whereas she should have been doing very gentle exercise - walking, swimming, nothing extreme - instead she had to take part in everything, and suffered a lot of pain at the time as well as the long term ramifications of ending up in a wheelchair. And as she didn't know any better, and because she'd always had pains and assumed it was normal, and thought that everyone else felt the same pains she did, she ended up doing what she was told.
Her dc have also got EDS - however they are 'lucky' in so far as it was identified very early on, their mum knows exactly how to treat them and how far to push them or not, and so on. The school is involved and knows - the sports staff know that they are not being lazy when they don't take part in everything or just do what they can, the matron knows their daily physio routine and helps them daily, their teachers don't expect them to do things they shouldn't - so instead of stacking chairs they might put out the pen pots for example, or if they go on a school trip they'll ensure they don't have to carry their lunch with them all morning or that if there's lots of walking they check they're ok or if they need a rest. It's not made into a big deal - but it's certainly something that is taken very seriously.
And that's the way it should be for your dd too.
I hope you manage to sort everything out and find a compromise that you're happy with and why on earth they are doing this in the first place - bet it's to save money as others have said.
oh and remember to include in your risk assessment things like the fact that your dd won't want to say no to a teacher so will do something even if she is in pain and then tell you about it later, so that relying on your dd to tell the teacher that she can't or shouldn't do something is not possible as she's too intimidated to tell the teacher how she really feels. And remember to include the cumulative damage worry - particularly to her wrists - which if she stresses early could lead to significant problems later in life - which in this day and age could be really significant because wrist problems often lead to problems with things like typing and writing which will be real problems when she is taking exams or when she wants to work write long MN posts! but can't type for as long as she needs to.
Sorry, I'll shut up now! Just good luck with getting it all sorted.