First sorry this family is being so disrespectful to you!Secondly, congratulations for standing up for your policies and standing up to her criticisms of you and your business.
No one tells me how things are going to go in my daycare. They can ask for something, but the decision is always mine.
The nerve of DCM to question your/our profession by calling you a babysitter. Obviously she thought she was humouring you by signing your contract and let you know this.
Some folks have really no clue how this business is run and how we have so many variables to content with.
Please continue to correct her comments if they don't sit well with you. If she continues this behaviour I would start looking for a replacement. This job can be difficult enough without being disrespected.