Hello, I am an attorney and am happy to assist.
Of course they can not force her to do this community service while she has a doctor's note saying she is not physically capable. That is ridiculous.
First you should send them a letter directly stating that she is not able to do this now, but will catch up when she is able. Attach the doctor's note again, and ask them to stop the process of asking her to leave.
Then you also need to send a formal letter to the housing authority, in addition to the prior letter to the management of the building, informing them of the situation and that they can not lawfully ask her to leave when she has a health condition that keeps her from doing this community service.
I would personally probably send the second letter in person, hand delivered, and insist on a meeting with someone high up in the housing authority, to try to get it taken care of right then and there. They know that can't do this, they are just trying to do it anyway, but if you get forward with them and direct, they should back down.
Let me know if you have questions about this before you rank my answer. If you don't, positive feedback with give me credit for my work with you today.