The amount of the adults in the house is really none of your concern as to assuming they have extra care when you are sick.
If a parent tried to give me a lecture on closing I would kindly let them know that this is my business and it is my descretion when to open and close based on the best interest of the kids in your care. If they are not happy with your policies they are welcome to find somewhere else to take their child. I would tell them that they are not welcome to come into my home and lecture me on sick days. I work for me, not them and if they are confused about that set up there is the door.
In regards to the late pick ups, no lunch etc. If you let things go like this then you are looked at as an employee and not the employer. You have set yourself up to be stepped on and talked down to. Review your policies with them and don't waiver a minute! Enforce a late fee for pick ups and for payment.
Oh... and post for a new client because you will not hang on to these people much longer... and you don't want them much longer either.