If you think you can work with the family as long as your conditions are better then you could try letting them know that as of whatever date you will no longer be doing such and such and the new rules will be the same as they are for everyone else in care. As you said it may make them walk. On the other hand the mom might just be the kind that comes across one way but didn't really mean to be - some have trouble treating people at the office one way and us another and they may realize they are ok with things the way they are way. That sort of takes the pressure off you to let them go which could have them spreading bad about you. But if you make it so they decide to leave then facts are facts - no special treatment so they leave.
Either way you should put it in writing and hand it to them while at the same time verbally saying I have come to a decision that I need to make a few changes at my daycare starting with.... and then mention the issue. You can go into detail if the opportunity seems right or just tell them to read the letter and reply by email with questions. After that dealing with it all by email puts the conversation in writing but allows you to type things and erase and reword etc.
E-mails can be very dangerous as perception can go either way.