If you have not given permission for your children to leave the house with the babysitter, it is kidnapping, is it not? Whose vehicle was being used? If it was your vehicle, there's also a possible charge of Grand Theft Auto if you did not give permission for her to take a JW joyride in your car. If it was someone else's car, how were your young children secured in child safety seats? Are they not REQUIRED by LAW to be in car seats up to a certain age when they are passengers in a vehicle for personal use? Does she have a key to your house? If not, did she leave your home unlocked and vulnerable to robbery while she was out in service?
There are just so many potential issues involved with her leaving the house with the children without your permission, and significant risks to your children, that you have to address them immediately and put a stop to this insanity.
If you are paying for babysitting services, it is highly unethical for the babysitter to remove the children from the home for activities in the babysitter's personal interests. It is YOUR responsibility and YOUR WIFE'S responsibility to provide religious education and training to YOUR CHILDREN, not HERS. If you are not paying, then I'd say you're getting what you pay for.
I'd make it crystal clear if you decide to use that sitter again: She is NOT to leave your home with your children (unless the house is on fire, obviously), nor is she to bring people into your home (ie, Bible Studies) while she is WORKING for you. Get a safe and put the spare car and house keys inside - she should not have a key to your house, nor should she have the keys to your car - you are asking for an insurance nightmare if she gets into an accident with your car or leaves the house unlocked and something bad happens.