Instead of turning the children away, why not explain to the mother that you simply don't have enough money for the extra children and they are welcome to stay if the mother can pay their way? Seems a little less harsh than sending the children home and leaves the ball (and embarrassment) in the other mother's court instead of yours. Also, I think it would be a good idea to specify these types of things on the invite, as the mother of 2 small children it is often difficult to get the older one to an activity without taking the younger one. Our preschool does similar things with field trips, citing the fee for any additional siblings/adults but paying the way of the preschooler and one adult. Most mothers completely understand the need for a budget if you make it known.