You will be a couple of days short for moving between two spots. The 14th day you leave one site will be the first day on the second site so at the end of the second 14th day stay you will have been only 27 days away from the first location.
I doubt anyone is watching that closely unless you really piss off a ranger.
If you vacate on Day 14 you will have only stayed 13 nights.
I had a NF ranger approach me after someone had made a complaint that I had overstayed, it was a nice spot. I explained, "last night was my thirteenth night, tonight will be my fourteenth night, and I will be leaving tomorrow." His response, "Oh, then you know about the 14 day rule." His interest in me waned at that point.
I went through this exercise years ago, setting up a spreadsheet to be used for trip planning. Had forum members telling me that I was crazy when I mentioned that there was something off about the 14 day rule. Change "day" to "night" and it becomes clear.
For example, arrive on March 1. After 14 nights it will be March 15. You have not violated spacetime.
Second site goes from March 15 to March 29.
March 29 is 28 days after arriving on March 1. You may safely move back to site 1 after 28 days, on March 29. No filler required.
You arrive on Day 1, spend your first night, and wake up on day 2, then spend your second night. Rinse, repeat until you wake up on Day 15 after your 14th night.
Day 15 becomes Day 1 when you arrive at the second site. Rinse, repeat.
If you are in IT you could call the first day Day Zero, then you would vacate on Day 14. The day you arrive doesn't count. The clock starts with the first night.
The regs were poorly written using "days" instead of "nights". The nights between the days is the important commodity that has to be limited.
As I said before, at this point in time, they are not going to spend a sizable portion of their limited budgets on the red tape required for changing one word for another.