Nested AND function within IF function is only addressing logical1 but not logical2

I have a spreadsheet where I've entered this equation

=IF(X2,'Leader Cost'!G11,IF(AND($A2<>"",AND($A2<>"First",$C2<>"Last"),AND($A2<>CoLeaderFirstName,$C2<>CoLeaderLastName)),AdminFee,"")).

Everything functions properly except the AND($A2<>"First",$C2<>"Last".

Just to clarify what X2 in the formula references, it's another formula that states =AND($A2=CoLeaderFirstName,$C2=CoLeaderLastName).

If there is a name in A2 and C2, there should be an AdminFee in the cell, if I type First in cell A2 and Last in cell C2 the cell should be blank according to the formula, but when I type First in cell A2 with anything typed in C2 the cell goes blank. It looks like it is not addressing logical2 in the AND function. I'm starting to think my understanding of the order Excel processes these arguments is incorrect, so any help would be great!

BTW, First and Last were originally LeaderFirstName and CoLeaderLastName, but I changed it to help work through what is going wrong.