I think I understand now:
you want to now if 2 (or 3?) variables are associated, controlling for another variable.
At t1, you see that there is no association at all between 2 of the variables, at T2, all variables are associated.
Variable1 +Variable 2 = related
Variable1 + Variable 3 = unrelated
Variable 2 + Variable 3= related
you want to know if you should still control for variable 3 in the relation between variable 1 and variable 2, given that variable 1 and varialbe 3 are unrelated at T1, is that correct?
In addition, you state:
The theory and my hypothesis did not support all variables being related
My first question is: why would you test it then?
Second, you know that the variables are all related at t2, thus, there is still a possiblity that the relation between V1 and V2 are partly due to overlap with V3 (even if this relation does not reach significance at T1). So I think it would be better to still control vor variable 3, even if it does not reach significance (because you know it could in fact have an impact, based on T3).
Also, this decision should not be based solely on statistics, but also on theory. Apparently you have a reason to control for V3, otherwise you would not have included it, right?