A couple of questions--
What ages are the children you are travelling with?
Will you go to the parks everyday that you are there?
Assuming the 3 kids are under 10, you could buy an AP for yourself to get the AP rate at CBR, and 7-day park hopper pluses for the kids from Connections for a grand total of 1619.42 (that is pre-tax on the room).
Using the package in July, you would pay somewhere around 1577.95, I think. So, the package would be a little cheaper. However, you would not have an AP. Any unused days with the Package would expire, while any unused days on the hoppers would be good forever. Have fun making up your mind!