Well, unfortunately, since you live in a state where partial homeschool isn't permitted, I think that you are going to have to opt for the laying low approach...
Maybe you and the teacher/admins who came up with the plan can meet periodically to discuss things which are working/not with the arrangement-- and mention that you aren't sure how they would prefer you explain this situation to curious onlookers (obviously official and with the school).
Should you refer to this as "I'm helping [Teacher] in the classroom?"
Or something else?
Is there a location where you "won't be disrupting others?"
(Yes, it's galling, that last one... but it is a way of subtly bringing up the fact that your DD deserves to have a learning environment that isn't shoved off in some corner of the faculty lounge!!!)
