Of course you have the right to ask her to stay at the door! I would explain why though...can you stay by the door in hopes of not spreading your illness to the other children. If you leave that part out then it may just seem rude!
There really isn't much you can do about families that get sick a lot. If they are following your sick child policy that is about all you can do.
I would feel it is ok to chat with them about helping to contain the illness. Making a quick drop off and pick up, keeping the sister at the door to prevent spread etc. They truly just may not have thought of it. Especially when they are sick and feeling crappy.