Hi Janna,
Once you activate your
four-day promotional theme park tickets on your first day of use, you are not required to use all four days of admission in succession. You may, as you note in your question, visit the theme parks on Monday, Tuesday, Saturday, and Sunday of the same week. Because these tickets do not have the no expiration option, you will need to use them within 14 days of activation but your plan falls comfortably within those parameters.
Admission to the Disney water parks (Typhoon Lagoon and Blizzard Beach) can be on the same days or separate days from the days you enter the four main Disney theme parks (Magic Kingdom, Disney's Hollywood Studios, Epcot, and Disney's Animal Kingdom). If, for instance, you enter Epcot and Blizzard Beach in the same day, it would subtract one day at the theme parks and one admission to a water park from your tickets. If on another day you enter both DisneyQuest and Blizzard Beach, that would subtract two more admissions from your Water Parks Fun & More plan. Note they are counting the times you enter these attractions rather than the number of days.
If you need additional advice as you plan your trip, please don't hesitate to post follow-up questions. The Moms Panel would be delighted to help.
Jill
PS. Thanks to your family for the service you provide to our country.