I agree with Brights ... no need to tell her WHY just that you wish you could help but it is not going to work.

Something like 'oh I am really sorry but in anticipation in X's last day giving me lower numbers for a while I have decided to take advantage of that and made field trip / outing plans for the program that week that will not accommodate having an extra child in tow." .... this would be the truth for me because when I know I am going to be low I tend to plan some of the bigger awesome venues available in my home town for a 'treat'.